U.S. patent number 10,459,212 [Application Number 15/744,672] was granted by the patent office on 2019-10-29 for optical trap for rheological characterization of biological materials.
This patent grant is currently assigned to The United States of America, as represented by the Secretary, Dept. of Health and Human Service. The grantee listed for this patent is The United States of America, as represented by the Secretary, Department of Health and Human Services, The United States of America, as represented by the Secretary, Department of Health and Human Services. Invention is credited to Benjamin Blehm, Alexus Devine, Kandice Tanner.
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United States Patent |
10,459,212 |
Tanner , et al. |
October 29, 2019 |
Optical trap for rheological characterization of biological
materials
Abstract
Systems and methods for assaying the viscoelastic properties of
a heterogeneous material are provided. The systems and methods
allow for application of an in situ calibrated optical trap to
optical trap beads within the material to assay the viscoelastic
properties. In several embodiments, the material can be a
biological material, such as tumor tissue or skin tissue.
Inventors: |
Tanner; Kandice (Rockville,
MD), Blehm; Benjamin (Oro Valley, AZ), Devine; Alexus
(Bethesda, MD) |
Applicant: |
Name |
City |
State |
Country |
Type |
The United States of America, as represented by the Secretary,
Department of Health and Human Services |
Bethesda |
MD |
US |
|
|
Assignee: |
The United States of America, as
represented by the Secretary, Dept. of Health and Human Service
(Bethesda, MD)
|
Family
ID: |
56684268 |
Appl.
No.: |
15/744,672 |
Filed: |
July 29, 2016 |
PCT
Filed: |
July 29, 2016 |
PCT No.: |
PCT/US2016/044850 |
371(c)(1),(2),(4) Date: |
January 12, 2018 |
PCT
Pub. No.: |
WO2017/020006 |
PCT
Pub. Date: |
February 02, 2017 |
Prior Publication Data
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Document
Identifier |
Publication Date |
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US 20180202913 A1 |
Jul 19, 2018 |
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Related U.S. Patent Documents
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Application
Number |
Filing Date |
Patent Number |
Issue Date |
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62198554 |
Jul 29, 2015 |
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Current U.S.
Class: |
1/1 |
Current CPC
Class: |
G02B
21/32 (20130101); G01N 11/00 (20130101); G01N
11/16 (20130101); A61B 5/0091 (20130101); A61B
5/445 (20130101); G01N 2011/008 (20130101); G01N
2203/0089 (20130101); G01N 2203/0094 (20130101) |
Current International
Class: |
G02B
21/32 (20060101); G01N 11/16 (20060101); G01N
11/00 (20060101); A61B 5/00 (20060101) |
References Cited
[Referenced By]
U.S. Patent Documents
Other References
Blehm, et al. "In vivo tissue has non-linear rheological behavior
distinct from 3D biomimetic hydrogels, as determined by AMOTIV
microscopy," Biomaterials, 83:66-78, 2016. cited by applicant .
Brau, et al. "Passive and active microrheology with optical
tweezers." Journal of Optics A: Pure and Applied Optics 9, No. 8
(2007): S103. cited by applicant .
Capitanio, et al. "Interrogating biology with force: single
molecule high-resolution measurements with optical tweezers."
Biophysical Journal 105, No. 6 (2013): 1293-1303. cited by
applicant .
Elkin, et al. "Mechanical heterogeneity of the rat hippocampus
measured by atomic force microscope indentation." Journal of
Neurotrauma 24, No. 5 (2007): 812-822. cited by applicant .
Fabry, et al. "Time scale and other invariants of integrative
mechanical behavior in living cells," Physical Review E, 68:041914,
2003. cited by applicant .
Fabry, et al. "Scaling the microrheology of living cells," Physical
Review Letters, 87: 148102, 2001. cited by applicant .
Fischer, et al. "Calibration of trapping force and response
function of optical tweezers in viscoelastic media," Journal of
Optics A: Pure and Applied Optics, 9:S239-S250, 2007. cited by
applicant .
Fischer, et al. "Active-passive calibration of optical tweezers in
viscoelastic media," Review of Scientific Instruments, 81:015103,
2010. cited by applicant .
Jun, et al. "Calibration of optical tweezers for in vivo force
measurements: How do different approaches compare?" Biophysical
Journal, 107:1474-1484, 2014. cited by applicant .
Keikha, et al. "Multi-frequency technique for frequency response
measurement and its application to servo system with friction."
IFAC Proceedings vols. 44, No. 1 (2011): 5273-5278. cited by
applicant .
Kim, et al. "Recapitulating the tumor ecosystem along the
metastatic cascade using 3D culture models." Frontiers in Oncology
5 (2015). cited by applicant .
Mas, et al. "Quantitative determination of optical trapping
strength and viscoelastic moduli inside living cells," Physical
Biology, 10:046006, 2013. cited by applicant .
Mizuno, et al. "Active and passive microrheology in equilibrium and
nonequilibrium systems." Macromolecules 41, No. 19 (2008):
7194-7202. cited by applicant .
Norregaard, et al. "Optical manipulation of single molecules in the
living cell," Physical Chemistry Chemical Physics, 16:12614-12624,
2014. cited by applicant .
Sarshar, et al. "Comparative study of methods to calibrate the
stiffness of a single-beam gradient-force optical tweezers over
various laser trapping powers," Journal of Biomedical Optics,
19.115001-115001, 2014. cited by applicant .
Shindel, et al. "Frequency modulated microrheology," Lab on a Chip
15, No. 11 (2015): 2460-2466. cited by applicant .
Tassieri. "Linear microrheology with optical tweezers of living
cells `is not an option`!" Soft Matter, 11:5792-5798, 2015. cited
by applicant.
|
Primary Examiner: Smith; Maurice C
Attorney, Agent or Firm: Klarquist Sparkman, LLP
Parent Case Text
CROSS REFERENCE TO RELATED APPLICATIONS
This is the U.S. National Stage of International Application No.
PCT/US2016/044850, filed Jul. 29, 2016, which was published in
English under PCT Article 21(2), which in turn claims the benefit
of U.S. Provisional Application No. 62/198,554, filed Jul. 29,
2015. The provisional application is incorporated by reference
herein in its entirety.
Claims
It is claimed:
1. A method of assaying viscoelastic properties of a sample,
comprising: directing a detection beam to a bead embedded in the
sample, wherein the bead is an optical trap bead; detecting
movement of the bead by sensing a position of the detection beam
downstream of the bead; directing a trap beam on the bead to apply
an optical trap to the bead; detecting passive movement of the
trapped bead due to thermal motion; oscillating the trapped bead
relative to the sample with a complex waveform comprising a
predetermined combination of frequencies, wherein the bead is
oscillated along a plane transverse to a path of the detection
beam; detecting active movement of the trapped bead due to the
oscillation; and calculating a trap stiffness and a complex modulus
for the bead based on the detected passive movement and the
detected active movement.
2. The method of claim 1, wherein the complex waveform is composed
of a combination of frequencies that provide distinct
harmonics.
3. The method of claim 2, wherein the complex waveform comprises: a
combination of prime frequencies; or a combination of frequencies
that are a predetermined multiple of prime frequencies.
4. The method of claim 2, wherein the combination of frequencies
comprises: a set of prime frequencies from 3 to 101 Hz; or a set of
frequencies from 300 to 15700 Hz that are a predetermined multiple
of prime frequencies.
5. The method of claim 2, wherein the combination of frequencies
comprises set from 10 to 30 frequencies.
6. The method of claim 1, wherein the combination of frequencies
are offset in phase.
7. The method of claim 1, wherein oscillating the trapped bead
relative to the sample comprises oscillations in a linear range of
viscoelasticity of the sample.
8. The method of claim 1, wherein oscillating the trapped bead
relative to the sample comprises oscillations of no more than 200
nm.
9. The method of claim 1, wherein oscillating the bead relative to
the sample comprises oscillating the trap beam using an
acousto-optic deflector (AOD) when the sample remains
stationary.
10. The method of claim 1, wherein oscillating the bead relative to
the sample comprises oscillating a nanopositioning stage holding
the sample when the trap beam remains stationary.
11. The method of claim 1, wherein the trap beam and the sample are
held stable when the passive movement of the trapped bead due to
thermal motion is detected.
12. The method of claim 1, wherein the detection beam and the trap
beam are directed on the bead through a water immersion
objective.
13. The method of claim 12, wherein the water immersion objective
has a numerical aperture of about 1.2.
14. The method of claim 1, wherein the position of the detection
beam downstream of the bead is sensed using a position sensing
detector.
15. The method of claim 14, wherein the position sensing detector
is a quadrant photodiode.
16. The method of claim 14, further comprising calculating a change
in volts per nm of bead displacement for the position sensing
detector.
17. The method of claim 16, wherein calculating the change in volts
per nanometer of bead displacement for the position sensing
detector comprises: stepping the sample through the detection beam
using a nanopositioning stage when the optical trap is not applied
to the bead; and sensing the position of the detection beam
downstream of the bead using the position sensing detector.
18. The method of claim 16, wherein determining the change in volts
per nanometer of bead displacement for the position sensing
detector comprises: oscillating the detection beam when the optical
trap is applied to the bead; and sensing the position of the
detection beam downstream of the bead using the position sensing
detector.
19. The method of claim 1, wherein the trap beam is a 1064 nm diode
laser and the detection beam is a 975 nm diode laser.
20. The method of claim 1, wherein the optical trap comprises a
trap power of 1-500 mW and a trap force of 1-10000 Pa.
21. The method of claim 1, wherein the bead is a fluorescent bead
and/or is about one .mu.M in diameter.
22. The method of claim 1, wherein the sample is a biological
material.
23. The method of claim 22, wherein the biological material is a 3D
tissue culture sample.
24. The method of claim 22, wherein the biological material is a
tissue sample.
25. The method of claim 24, wherein the tissue sample is a tumor
sample.
26. The method of claim 1, comprising assaying the viscoelastic
properties of: extracellular remodeling during development and
cancer metastasis; keloid scar formation during wound healing;
repair and regeneration of injured collagenous tissues such as
tendon and cartilage; skin stiffening or softening due to aging or
other conditions; scar formation as scar stiffen or soften due to
treatment; collagen fibrils and networks in vitro; and/or in vivo
mechanical mammography.
Description
FIELD OF THE DISCLOSURE
This relates to embodiments of systems and methods for applying an
optical trap to a bead embedded in a sample to assay the
viscoelastic properties of the sample.
BACKGROUND
The viscoelastic properties of a material (such as a biological
material), are the resistance to flow (viscosity) and the
resistance to deformation (elasticity) of the material. Viscous
materials resist shear and strain linearly with time upon
application of stress. Elastic materials strain when stretched and
return to their original state when the stress is removed.
Viscoelastic materials have elements of both of these properties
and, as such, exhibit time-dependent strain. The storage and loss
modulus (the "complex modulus") in viscoelastic materials measure
the stored energy, representing the elastic portion, and the energy
dissipated as heat, representing the viscous portion. Biological
materials are rarely just viscous or just elastic, and typically
display a combination of viscoelastic properties.
An optical trap includes a focused laser beam able to trap small
particles at its focus, and can be used to interrogate the
viscoelastic properties of certain materials. However, issues of
image resolution and limited depth of interrogation have prevented
use of optical trap techniques to measure viscoelastic properties
in certain materials, such as biological materials including
multi-cellular systems and tissue in living organisms.
SUMMARY
The methods and systems disclosed herein involve the use of an
optical trap to evaluate the viscoelastic properties of a sample,
such as a biological material. Using the disclosed systems and
methods, it is possible, for the first time, to interrogate the
viscoelastic properties of in vivo and ex vivo tissue using optical
trap-based microrheology.
In some embodiments, a method of assaying viscoelastic properties
of a sample is provided. The sample can be, for example, a
biological material, such as a 3D tissue culture sample, an in vivo
or ex vivo tissue sample, and/or a tumor sample. The method
comprises directing a detection beam to an optical trap bead
embedded in the sample, and detecting movement of the bead by
sensing a position of the detection beam downstream of the bead. A
trap beam is directed on the bead to apply an optical trap to the
bead. Passive movement of the trapped bead due to thermal motion is
detected. The trapped bead is oscillated relative to the sample
with a complex waveform comprising a predetermined combination of
frequencies, wherein the bead is oscillated along a plane
transverse to a path of the detection beam. The active movement of
the trapped bead due to the oscillation is detected. Based on the
detected passive movement and the detected active movement, a trap
stiffness and a complex modulus for the bead are calculated.
In some embodiments, the complex waveform used to oscillate the
bead comprises a combination of frequencies that provide distinct
harmonics, such as a set of prime frequencies of from 3 to 101 Hz,
for example a set of 20 frequencies of from 3 to 101 Hz. In some
embodiments, the complex waveform used to oscillate the bead
comprises a combination of frequencies that are a predetermined
multiple of prime frequencies, such as a set of frequencies of from
300 to 15700 Hz that are a predetermined multiple of prime
frequencies. In some embodiments, the frequencies in the
combination of frequencies are offset in phase. Use of a complex
waveform composed of a combination of frequencies with distinct
harmonics to oscillate the bead reduces
Oscillating the trapped bead relative to the sample preferably does
not exceed a linear range of viscoelasticity of the biological
material. In some embodiments, oscillating the trapped bead
relative to the sample comprises oscillations of no more than 200
nm.
In some embodiments, oscillating the bead relative to the sample
comprises oscillating the trap beam using an acousto-optic
deflector (AOD) when the sample remains stationary. In other
embodiments, oscillating the bead relative to the sample comprises
oscillating a nanopositioning stage (such as a piezo stage) holding
the sample when the trap beam remains stationary.
Several embodiments comprise calculating a change in volts per nm
of bead displacement for a position sensing detector (PSD), such as
a quadrant photodiode (QPD), that detects the position of the
detection beam downstream of the optical trap bead. In some
embodiments, calculating the change in volts per nanometer of bead
displacement for the PSD comprises stepping the biological material
through the detection beam using a nanopositioning stage when the
optical trap is not applied to the bead, and detecting the position
of the detection beam downstream of the bead using the PSD. In
other embodiments, calculating the change in volts per nanometer of
bead displacement for the PSD comprises oscillating the detection
beam when the optical trap is applied to the bead; and sensing the
position of the detection beam downstream of the bead using the
PSD.
In some embodiments, the disclosed method of assaying viscoelastic
properties of a sample can be used to assay the viscoelastic
properties of extracellular remodeling during development and
cancer metastasis, keloid scar formation during wound healing,
repair and regeneration of injured collagenous tissues such as
tendon and cartilage, skin stiffening or softening, scar formation
as scar stiffen or soften due to treatment, collagen fibrils and
networks in vitro; and/or in vivo mechanical mammography.
The foregoing and other features and advantages of this disclosure
will become more apparent from the following detailed description
of several embodiments which proceeds with reference to the
accompanying figures.
BRIEF DESCRIPTION OF THE FIGURES
FIG. 1 is a schematic diagram illustrating aspects of an embodiment
of an optical trap system for use with the disclosed methods.
FIG. 2 is a flow chart illustrating an exemplary embodiment of a
process for assaying viscoelastic properties of a sample.
FIG. 3 is a schematic diagram illustrating aspects of an embodiment
of an optical trap system for use with the disclosed methods.
FIGS. 4A and 4B show a set of schematic diagrams and graphs
illustrating bulk rheology and microrheology. (4A) Schematic of the
method to obtain rheological parameters of materials using an
optical trap. The optical trap is composed of a trapping laser
(dark grey) and a detection laser (light grey). The trapping laser
is used to actively modulate a single bead (middle panel) with high
spatial resolution. In a bulk rheometer (right), sample material
.about.1 mm thick is sandwiched between rigid parallel plates, and
rotational shear is applied at various amplitudes and frequencies.
(4B) Microrheology measurements (left), enlarged at low frequencies
(middle), and bulk rheology measurements at the low frequencies
(right) in matrigel and HA (n=3 separate samples for each
measurement).
FIGS. 5A-5D are a set of graphs showing that active optical
trapping microrheology in matrigel and zebrafish resolves
viscoelastic properties with high spatial resolution over a wide
range of frequencies. An optical trap was used to perform
multiplexed rheology measurements spanning frequencies from 3 to
15700 Hz in (5A) Matrigel (n>15), (5B) HA (n>15), and
zebrafish (5C) brain (n>5) and (5D) tail (n>5). The
trap-induced displacements of beads of diameter 1 mm were converted
to storage (elastic) and loss (viscous) moduli using four different
calibrations: with individual calibrations of the stiffness and
volts-to-nanometers of each bead in situ (4); averaged stiffness
over all beads measured (3); the average stiffness of the same
beads calibrated in water using the power spectrum method (2); and
the average volts-to-nanometers conversion for the QPDs calibrated
in water (1). These comparisons demonstrate the improved accuracy
of our technique. In addition, the right-most panels show high
frequency linear fits to the data, where in 5A) the linear fits are
all better than R2 of 0.98, and the lines' slopes are all
significantly different (p<0.01), in 5B) HA, the linear fits are
>0.98 for the loss moduli, and 0.92 for the storage moduli, with
the lines' slopes again all significantly different (p<0.01). In
(5C-5D), a similar comparison for data obtained in the tail (5C)
and brain (5D) in the zebrafish is shown. Graphs depict averages
over bead measurements, with the mean and (symbols) /% standard
error of the mean. For each sub figure, right panel shows the
linear regression fits with >0.98 R2 in the loss modulus
(bottom), and >0.93 in the storage (top). The lines' slopes were
once again significantly different to a (p<0.01). Comparison of
different calibration methods over all frequencies in all samples
are also significantly different, as determined by the
non-parametric Friedman test with p<0.0001.
FIG. 6 is a set of graphs showing the estimation of complex moduli
by calibration method. Calculation of G' and G'' using the average
trap stiffness (k) or average volts-to-nanometers conversion factor
(.beta.) from either the sample or from water results in
overestimation of G' and G''. At each measured frequency, the mean
G' calculated from each calibration method was divided by the mean
G' calculated from in situ calibration, yielding the overestimation
factor; no frequency dependence was observed, so the values were
averaged over all frequencies. Mean.+-. standard deviation shown
for each method applied to data from Matrigel, HA, zebrafish tail
and brain. All alternate calibrations differ from our technique
significantly (p<10.sup.-26).
FIGS. 7A-7E show a schematic diagram and a set of graphs
illustrating results from applying varied stresses using optical
trap microrheology reveals differential responses in Matrigel and
HA. (7A) There are two ways to vary the stress applied to the
bead's microenvironment using the trapping laser: by changing the
amplitude of the oscillation per frequency (left) and by changing
the laser power (right). The maximum displacement of the bead can
be likened to the strain induced in bulk rheometers. (7B-7C) show
the response of Matrigel and HA, respectively, to these different
types of stress (averaged over n>3 samples, # beads>15 per
gel). One condition where only the amplitude of oscillation is
changed (left, 2 nm and 20 nm) and the other where the trap laser
power is changed (10 mW, 100 mW and 500 mW) at a constant amplitude
of oscillation 20 nm (right) lead to significantly different values
of G' (top) and G'' (bottom) as determined by the non-parametric
Friedman test p<0.0001. In addition, at about 1000 Hz, all data
is fitted with a power law (A.omega..sup.B), which revealed
significantly different exponents at different powers for the
storage moduli (p<0.01). Matrigel typically had exponents of
approximately 0.3 in the storage modulus, and 0.6 in the loss
moduli, HA storage moduli exponents ranged from 0.47 at 10 mW to
0.29 at 500 mW. The loss moduli were all around 0.7 however, near
the expected value for a semi-flexible polymer. (7D-7E), Bulk
rheology in HA and Matrigel at different strains for comparison to
microrheology data (n=3 samples).
FIGS. 8A and 8B are a set of graphs showing that zebrafish tissue
displays non-linear behavior with tissue viscoelasticity depending
on the applied stress. Storage (elastic, top) and loss (viscous,
bottom) moduli, measured for an average over n>3 zebrafish,
number of beads>10 per tissue, per fish, located in the brain
(8A) and tail (8B) at different trapping laser powers (10 mW (1);
100 mW (2); 500 mW (3)) where the amplitude of the bead oscillation
is 2 nm on the left, and 2 nm on the right. Different oscillation
and trap amplitudes in G' and G'' in the tail or brain are
significantly different as determined by the non-parametric
Friedman test (p<0.01). The data also displayed a wide range of
exponents from the power law fits, ranging from 0.4 to 0.8 in the
various conditions. Graphs depict averages over samples (zebrafish
or hydrogels), with the mean and (symbols).+-.standard error of the
mean.
FIGS. 9A and 9B are a set of graphs showing results of QPD voltage
to nm bead displacement calibration. (9A) Measurements across the
entire range of piezo stage positions, showing the
tapering/nonlinearities at the edges of the range. (9B)
Measurements across a linear range.
FIGS. 10A and 10B are a set of graphs showing a comparison of
single frequency sweeps to multiplexing of frequencies in Matrigel
at different laser powers. Modulation of trapping power allows the
probing of different material properties and gives the equivalent
of stress strain curves required to quantitate force responses in
materials. In addition, multiplexing gives comparable measurements
to single frequency sweeps. FIG. 10A shows graphs of individual
frequency sweeps, while FIG. 10B shows graphs of multiplexed
frequency assays. The data shown in the FIG. 10A required 20
minutes per bead, while data shown in FIG. 10B was acquired in 40
seconds.
FIGS. 11A and 11B are a set of graphs showing a comparison of
single frequency sweeps to multiplexing of frequencies in Matrigel
at different laser powers in the zebrafish. Modulation of trapping
power allows the probing of different tissue properties and gives
the equivalent of stress strain curves required to quantitate force
responses in materials. In addition, multiplexing gives comparable
measurements to single frequency sweeps. FIG. 11A shows graphs of
individual frequency sweeps, while FIG. 11B shows graphs of
multiplexed frequency assays. The data displayed in FIG. 11A
required 20 minutes per bead, while data shown in FIG. 11B was
acquired in 40 seconds.
FIGS. 12A-12D are a set of graphs illustrating that in
situ-calibrated optical trap based active microrheology resolves
nonlinear stress-strain behavior in tumor samples. Active
microrheology of excised murine subcutaneous melanoma tumors.
B16-F10 metastatic mouse melanoma cells or MDA-MB-231 breast cancer
cells were subcutaneously injected with fluorescent polystyrene
microspheres into the flank and tumors were allowed to grow for 2
weeks. Animals were sacrificed and tumors were excised, rinsed, and
thin sections (.about.70 .mu.m) prepared on glass bottom dishes for
measurements. (12A and 12B) Storage (12A) and loss (12B) moduli vs.
frequency at oscillation amplitudes 2 nm (1), 5 nm (2), 10 nm (3),
and 20 nm (4) for B16-F10 metastatic mouse melanoma cell tumor
samples are shown. Additionally, the Complex modulus vs. frequency
(G' and G'') for (12C) B16-F10 metastatic mouse melanoma samples or
(12D) MDA-MB-231 breast cancer cell tumor samples using Oscillation
amplitude of 20 nm per frequency is also shown.
FIGS. 13A-13C show a set of diagrams illustrating calibration for
active microrheology in vivo. (13A) Determining micromechanical
properties of interest can include calibration of the optical trap
stiffness, K, and the positional sensitivity .beta. (the V-nm
conversion factor) of the detection system used to measure probe
displacements. (13B) Because probes lie in different positions
along the beam axis and in regions with different optical
properties, measurements in vivo (such as in the depicted zebrafish
embryo) require that both of these calibrations be conducted for
every probe measured in the sample. In some regions, probes may be
free to fluctuate in position because they are not tightly confined
(e.g. in the viscous yolk), or are subject to flow (as in
perivasculature). (13C) Two methods used to calibrate .beta. are
(1) the thermal power spectral density (PSD) method and (2) the
piezo stage stepping method. In the PSD method, the probe is
trapped and allowed to fluctuate due to thermal motion while
voltage on the detector is recorded. Fluctuations in voltage are
related by .beta. to position fluctuations predicted by a
fluctuation-dissipation model assuming probe radius and the drag
coefficient, which is unknown. In the piezo stage stepping method,
the probe is stepped through the detection beam as the stage is
moved through known distances, while the voltage on the detector is
recorded. This works well unless the probe and stage motions are
not in tandem. FIG. 13C (3) To calibrate under such conditions, a
detection beam steering method in which the trap is used to hold
the probe stationary while the detection beam is scanned across the
probe and the measured voltage is used to find .beta..
FIG. 14 is a schematic diagram of an exemplary optical trap system.
Both the trap beam and the detection beam have two dimensional
acousto-optical deflectors (AOD) in the optical path, along with
the two telescope lens pairs (one pair is shared for both beams
after the dichroic) for collimation and mapping images onto the
detection QPD. With this system, a probe can be trapped and the
detection beam is steered across it while the detection QPD signal
is recorded to calibrate .beta.. Then trap beam can be alternately
oscillated and held stationary in a sequential measurement for both
the active-passive calibration of trap stiffness and for broadband
active microrheology measurements.
FIGS. 15A-15D illustrate methods for calibrating the V-nm
conversion factor .beta.. In the piezo stage stepping method, QPD
voltage is recorded while the stage is stepped through the
detection beam in defined steps (such as 12 nm steps) by moving the
sample stage via piezo controller. (15A) In viscoelastic solids,
the probe moves with the sample stage, so the recorded voltage
correctly corresponds to the linear response of the detector to the
interference pattern in the back focal plane of the condenser
caused by the probe. Linear regression is used to get .beta. from
the voltage and position data. (15B) In liquid or liquid-like
samples, the probe may move freely, and is not constrained to move
in tandem with the stage, so the signal cannot be used to find the
positional sensitivity. (15C and 15D) In the detection beam
steering method, the probe is first trapped and held stationary.
The detection beam is then steered using an acousto-optic
deflector, oscillating across the probe center with an amplitude of
.about.55 nm and frequency of 1 kHz while the QPD voltage signal is
recorded. To calculate .beta., the signal is Fourier transformed to
find the voltage at the drive frequency.
FIGS. 16A-16B are a set of histograms showing results from V-nm
conversion factors (.beta.) of carboxylated polystyrene
microspheres in water and hydrogels obtained by PSD and FIT
methods. Each probe was trapped and passive motion was recorded,
Fourier transformed and fitted to a Lorentzian power spectrum model
with the drag coefficient of water to calculate .beta.. Then the
detection beam was oscillated across the probe center with
frequency 1 kHz and amplitude 54.7 nm, Fourier transformed and used
to calculate .beta.. (16A) comparison of values from both methods.
(16B) Misapplication of the PSD method in elastic or viscoelastic
materials results in overestimation of .beta. values by as much as
factors of nearly 100. .beta..sub.PSD/.beta..sub.FFT is tightly
centered near unity with the PSD method only 1% greater on average,
with standard deviation and coefficient of variation <4%.
FIGS. 17A-17F. Active Microrheology data of probes in uncured PDMS
(17A-17C) and injected into the yolk of a zebrafish embryo at 48 h
post fertilization (17D-17F). Measurements were conducted from 2
Hz-12,863 Hz, with multiplexed frequencies at stress-strain
amplitudes of 2 nm, 5 nm, and 20 nm (trap displacements) per
frequency to probe the stress-strain behavior (17A,17D) Elastic
component of the complex shear modulus. (17B,17E) Viscous component
of the complex shear modulus. (17C,17F) Magnitude of the complex
shear modulus. The moduli increased significantly with increasing
stress-strain amplitude (p<0.0001, two-way ANOVA).
DETAILED DESCRIPTION
The methods and systems disclosed herein involve the use of an
optical trap to evaluate the viscoelastic properties of a sample,
such as a biological material. In optical trap-based microrheology,
small refractive probes are embedded in a sample to serve as local
microenvironment sensors. An optical trap is applied to the
embedded probe. Once trapped, the bead undergoes spring-like
oscillations if perturbed by an applied force, where the
displacement amplitude is related to the perturbing force by the
trap stiffness. Accurate deduction of material characteristics by
measurement of bead displacement requires that the trap stiffness
is known. For non-complex materials, the trap stiffness can be
estimated prior to an experiment by calibration in an appropriate
material that is assumed to have the same refractive index as the
sample. However, this approach is inapplicable to complex materials
(such as in vivo and ex vivo samples), as tissues are optically
heterogeneous and the refractive indices are unknown a priori.
To address issues associated with optical trap-based microrheology
of complex materials, such as in vivo and ex vivo materials,
modified optical trap-based microrheology systems and methods are
provided. Using the disclosed systems and methods, it is possible,
for the first time, to interrogate the viscoelastic properties of
in vivo and ex vivo tissue using optical trap-based microrheology.
This is a particularly surprising result, given that prior
teachings posited that such measurements were not possible (see,
for example, Tassieri, "Linear microrheology with optical tweezers
of living cells `is not an option`!," Soft Matter, 11:5792-5798,
2015).
An optical trap is a highly focused laser beam that provides an
attractive or repulsive force to hold and/or move an optical trap
bead having a dielectric charge in physical space. The laser beam
is typically focused on the particle by sending it through a
microscope objective. The narrowest part of the focused beam (the
beam waist) has a strong electric field gradient. The dielectric
optical trap bead is attracted to the strongest electric field on
the gradient, which occurs at the beam waist. The optical trap bead
is "trapped" when it is held in position by the force of the laser
beam at the beam waist. "Applying an optical trap" refers to
directing a laser beam to an optical trap bead under conditions
such that the optical trap bead is held in position at the beam
waist by electric field gradient of the focused beam. Once trapped,
the optical trap bead can be manipulated in physical space by
moving the trap beam relative to the sample containing the optical
trap bead. Preferably, the optical trap can be operated in such a
way that the dielectric particle does not move beyond the linear
range of viscoelastic deformation of the local environment
surrounding the bead.
Using the novel optical trapping procedures described herein,
significant improvements in spatial resolution and tissue depth
have been obtained, in particular for examining clinically relevant
samples such as a biological material. As used herein, a biological
material is a natural or synthetic material containing cells or
containing the products of cells (such as the extracellular
matrix). In some embodiments, the biological material can be a
tissue from a subject. A subject can be, for example, any
vertebrate animal, such as humans, non-human primates, pigs, sheep,
cows, rodents, zebrafish, and the like. In two non-limiting
examples, a subject is a human subject or a murine subject. In some
embodiments, the biological material can be the skin of a mammal
(such as a rabbit, a rat, a mouse, or human). In some embodiments,
the biological material can be a biological sample obtained from a
subject. Biological samples include all clinical samples useful for
detection of disease or infection (for example, cancer) in
subjects, including, but not limited to, cells, tissues, and bodily
fluids, such as blood, derivatives and fractions of blood (such as
serum), cerebrospinal fluid; as well as biopsied or surgically
removed tissue, for example tissues that are unfixed, frozen, or
fixed in formalin or paraffin. In some embodiments, the biological
sample is a tumor sample, such as all or a portion of a tumor and
its microenvironment.
The sample contains one or more embedded optical trap beads that
serve as a local sensors. As used herein, an optical trap bead is a
dielectric particle that can be manipulated using an optical trap.
In some embodiments, the optical trap bead can be a fluorescent
dielectric bead having a diameter of between 0.1 and 10 .mu.M (such
as 1 .mu.M). When applied to a sample for detecting and/or
manipulation using an optical trap, the optical trap bead is
preferentially monodispersed in the sample, for example, the
optical trap bead does not aggregate in the sample. In some
embodiments, the optical trap bead can be injected into a sample
(such as a tumor sample) prior to performance of the methods as
described herein. In some embodiments, the optical trap bead can be
a fluorescent bead. In some embodiments, the optical trap bead can
have an altered surface chemistry to target the bead as needed in a
material of interest. For example, the optical trap bead can have a
surface modification that targets the bead via ligand/receptor
interaction to a particular cell type in a subject. In some
embodiments, the optical trap bead can be linked to a binding
moiety that specificity binds to a tumor associated antigen to
target the bead to a particular tumor.
In some embodiments, the disclosed systems and methods can assay
viscoelastic properties of a sample, such as a biological material
at a penetration depth of up to 1000 .mu.M in the sample, such as
up to 500 .mu.M, up to 400 .mu.M, up to 300 .mu.M, up to 200 .mu.M,
up to 100 .mu.M, from 100-500 .mu.M, from 100-1000 .mu.M, from
200-1000 .mu.M, from 200-500 .mu.M, or from 300-700 .mu.M.
Compared to magnetic bead-based microrheology, the disclosed
systems and methods provide a localized, precise application of
force. Compared to passive, thermally driven-based microrheology,
the disclosed systems and methods have greater dynamic range, and
can probe outside the thermal energy range, measuring non-linear
effects at different length and energy scales. The viscoelastic
measurements obtained using the disclosed systems and methods have
a surprisingly high contrast-to-noise ratio compared to prior
methods of obtaining viscoelastic measurements for complex
materials, such as biological materials. The increased
contrast-to-noise ratio allows for more sensitive detection of
changes in viscoelastic properties across biological materials than
what was possible using prior methods. For example, using the
disclosed optical trapping systems and methods, the first
description of live vertebrate microrheology and tumor sample
microrheology was obtained and is provided herein. Thus, the
disclosed systems and methods can be used to measure the
microrheology of a wide variety of complex materials (such as
biological materials), from 3D tissue culture models to tissue in
or from living zebrafish to mammals, such as mice and humans.
FIG. 1 depicts aspects of an optical trap system for use with the
disclosed methods. The system includes a trap laser and a detection
laser. The trap laser produces a trap beam (solid line) that can be
directed to an optical trap bead in a sample to apply an optical
trap to the bead. The detection laser produces a detection beam
(dotted line) that can be directed to the optical trap bead in the
sample to detect movement of the bead relative to the sample.
As used herein, laser beam or beam refers to electromagnetic
radiation at wavelengths of between about 100 nm and 10 .mu.m, and
typically between about 500 nm and 2 .mu.m. Examples based on
available laser diode sources generally are associated with
wavelengths of between about 800 nm and 1700 nm. The trap and
detection lasers produce beams of appropriate wavelengths so that
the beams can be aligned and separated as needed for application of
an optical trap of a bead and detection of bead displacement. In a
non-limiting embodiment, the trap laser can be a 1064 nm diode
laser, and the detection laser can be a 975 nm diode laser. Optical
beams and optical elements are described in some examples with
respect to one or more axes. Typically, an axis includes one or
more straight line segments along which an optical beam propagates
or along which one or more optical elements are situated. Such axes
can be bent or folded with reflective surfaces, so that axes need
not be single straight line segments.
Typical laser diodes have emission regions having non-circular
cross-sections. An emission region of a laser diode can be
associated with a slow axis that is directed along a longest
dimension of the emission region and a fast axis that is directed
along a shortest dimension of the emission region. Along the slow
axis, an emitted beam tends to have a smaller angular divergence
than the angular divergence along the fast axis. In addition, the
slow axis tends to be associated with beam propagation in more
transverse modes than beam propagation in the fast axis so that a
beam parameter product (corresponding to a product of an angular
divergence and a beam dimension) measured along the slow axis is
larger than that measured along the fast axis. Beam divergences and
diameters along the slow axis, the fast axis, or both can be
adjusted with one or more lenses, prisms, or mirrors to provide
selected beam characteristics.
Continuing with the embodiment depicted in FIG. 1, the light path
of the trap laser is directed through an Acousto-Optic Deflector
(AOD), which can be used to oscillate the trap beam to oscillate
the trapped bead in the sample. The light path of the trap laser
then continues to a beam sampler which is used to separate a small
percentage of the beam, which is directed to a PSD (such as a QPD),
to determine the oscillation of the trap laser. The sum, left-right
difference, and top-bottom difference channel voltage readouts
sensed by the trap PSD can be obtained by analog input channels of
a data acquisition (DAQ) card in operable communication with the
trap PSD.
The light paths of the trap beam and the detection beam are then
directed to a dichroic mirror, which is used to align the paths of
the two beams and direct the aligned beams (illustrated using a
line with dashes and dots) towards the optical trap microscope.
In the illustrated embodiment, the microscope comprises an
objective, a stage holding the sample with the embedded optical
trap bead, and a condenser. In some embodiments, the objective can
be a water immersion objective with a high numerical aperture, such
as about 1.2. In some embodiments, the condenser can be a water
immersion condenser. In several embodiments, the microscope stage
can be a motorized stage for controlling movement in X, Y, and Z
dimensions, such as a nanopositioning stage. The stage is
configured for holding the sample, such as a biological material.
The microscope can include any additional standard components that
are useful for optical trap-based microrheology methods, such as a
CCD camera and corresponding lamp for assistance in positioning a
bead in the focal plane of the microscope objective.
As shown in FIG. 1, the aligned trap and detection beams pass
through the microscope objective and are directed to the sample
containing the optical trap bead before being collected by the
condenser. The trap and detection beams are focused by the
objective on the optical trap bead in the sample mounted on the
stage of the microscope. Typically, the trap beam has a width that
slightly overfills back aperture of the microscope objective,
whereas the detection beam has a width that is smaller than the
trap beam's width, and does not fill the back aperture of the
microscope objective.
The trap beam and the detection beam are collected by the
condenser. The light path from the condenser then passes through an
emission filter that allows passage of the detection beam, but not
the trap beam. In an alternative embodiment, the light path from
the condenser can pass through a dichroic mirror that separates the
trap and detection beams. The light path of the detection beam
continues to a PSD (such as a QPD), to determine the position of
the detection beam. The sum, left-right difference, and top-bottom
difference channel voltage readouts sensed by the detection PSD are
obtained by analog input channels of the DAQ card.
Time-correlated trap and probe QPD signals are recorded on the DAQ,
which also controls radio frequency signals that drive the AOD.
FIG. 2 depicts an embodiment of a disclosed method for assaying
viscoelastic properties of a sample, such as a biological sample,
using an optical trap. Using this method, it is possible for the
first time to interrogate the viscoelastic properties of in vivo
and ex vivo tissue samples using an optical trap.
When a laser beam focuses on a bead, refraction-induced changes in
the momentum of light produce a harmonic potential within the
laser's focal volume, trapping the bead in a force field such that
it undergoes spring-like oscillations about the trap center if
perturbed by an applied force, where the displacement amplitude of
the bead .DELTA.x is related to the perturbing force F by the trap
stiffness k by F=-k.DELTA.x. Accordingly, accurate deduction of
force F by direct measurement of bead displacements requires that
trap stiffness k is known. In several embodiments, the disclosed
methods of assaying viscoelastic properties of a sample, such as a
biological sample, using an optical trap, provide superior
procedures for calibrating the trap stiffness for a bead embedded
in a sample.
Prior to performance of the disclosed methods, the optical trap
system can be calibrated as needed using standard methods. For
example, the optical trap system can be calibrated for alignment
and functionality using a control sample containing embedded
optical trap beads.
As shown in FIG. 2 at process block 102, the embodiment comprises
directing a detection beam on an optical trap bead embedded in a
sample, such as a biological material. The sample is typically
mounted on a stage on a microscope included in an optical trap
system, such as described herein. Directing the detection beam on
the optical trap bead can comprise directing a detection beam of
appropriate wavelength through a microscope objective to be focused
on an optical trap bead embedded in a sample.
As shown in process step 104, movement of the bead is detected by
sensing a position of the detection beam downstream of the bead.
One way to measure probe displacements in optical trap systems is
by back focal plane interferometry (see, e.g., Denk and Webb, AppL
Opt., 29(16) 2382-2391 (1990); and Allersma et al., Biophys. J.,
74(2) 1074-1085 (1998), each of which is incorporated by reference
herein). When a probe of diameter d is trapped at the center of the
beam waist of a laser with wavelength .lamda. focused by an
objective in its image plane, some light undergoes scattering due
to light-probe interactions and (in the dipole limit d<.lamda.)
produces spherical waves. This scattered light slightly diverges
from the fraction of light that does not undergo scattering. Thus,
shifts in relative phase between these two wavefronts give rise to
a pattern of constructive and destructive interference. A condenser
collects this light, and is placed such that the image planes of
the field diaphragm iris and the objective are conjugate and image
into each other (forming a Keplerian telescope). Behind the
condenser, a dichroic mirror or emission filter separates the
detection beam (but not the trap beam or lamp light) onto a
detection lens that is positioned to relay the image at the back
focal plane of the condenser onto a PSD, such as a QPD. In this
configuration, displacements of the probe cause rotation of the
detection beam in the image plane and corresponding translations of
the beam at both the back-aperture of the condenser and on the
detection QPD. The interference pattern is mapped onto the QPD; so
lateral displacements of the probe relative to the detection beam
in the imaged plane result in changes in voltage. The voltage
response .DELTA.S.sub.x is linearly related to probe translations
for small displacements (.DELTA.x.+-..about.150 nm from the probe
center). Thus, calibrating the position detection sensitivity
consists in finding the V-nm relation .DELTA.x=.beta..DELTA.S.sub.x
in the linear response regime.
The PSD preferably can be calibrated for each optical trap bead to
determine a change in volts per nm of bead displacement (V-nm
conversion) detected by the PSD for that particular bead. In
several embodiments, the change in volts per nanometer of bead
displacement, .beta., is calculated for the PSD (such as a QPD)
that senses movement of the detection beam downstream of the bead.
Exemplary methods for determining .beta. for particular bead
embedded in a sample are provided in the Examples below. In some
embodiments, this calibration step comprises, stepping the bead
through the detection beam by moving the stage holding the sample
in x and y dimensions (for example, 10 nm per step, 11 steps). This
step is performed when the bead is not trapped by the trap beam.
The PSD voltage can be recorded and normalized to the sum of the
total voltage on the PSD for each dimension (x and y). A condenser
collects scattered light from the bead and the conjugate image of
the bead is mapped onto the back-focal plane and collected on the
PSD. A line fit to the data is used to obtain a volt to nanometer
conversion in both dimensions (x and y). Exemplary procedures for
determining volt to nanometer calibrations for an optical trap bead
are described in Examples 1 and 3. In some embodiments, a detection
beam steering approach is utilized for determining .beta., as
described in Example 3 below. The detection beam steering approach
uses a weak detection beam to scan across the probe while it is
confined in the optical trap for determining .beta. for a
particular optical trap bead. The detection beam steering approach
is particularly useful for determining .beta. when the bead of
interest is either weakly attached to or freely moving through the
sample microenvironment, such as in the perivascular
microenvironment in the zebrafish trunk. The detection beam
steering approach is also useful for calibrating .beta. for optical
trap beads that are strongly attached or confined in a solid-like
microenvironment, and the microenvironment may be nonlinear,
viscous, elastic or viscoelastic with unknown Brownian
dynamics.
At process step 106, a trap beam is directed to the optical trap
bead in the sample. Typically, a microscope objective is used to
focus the trap beam on the bead. After passing through the
microscope objective, the trap beam forms a beam waist, and the
optical trap bead is attracted to the position of the beam waist by
electric field gradient. Once "trapped," the movement of the bead
due to passive (thermal) motion can be assayed by detecting the
position of the detection beam downstream of the bead, for example,
using the PSD. Additionally, the optical trap bead can be
manipulated in physical space by moving the trap beam relative to
the sample, and the movement of the bead due to this active motion
can also be assayed by detecting the position of the detection beam
downstream of the bead, for example, using the PSD.
As shown in FIG. 2 at process step 108, the passive movement of the
bead due to thermal motion is detected. For this step, the optical
trap is applied to the bead, and motion of the bead when the sample
and the trap beam are held steady is assayed by detecting the
position of the detection beam downstream of the bead. In some
embodiments, the thermal power spectrum of the bead's passive
thermal motion P.sub.U(.omega.) can be recorded as:
P.sub.U(.omega.)={tilde over (x)}.sub.U(.omega.)|.sup.2, equation
(1) where {tilde over (x)}.sub.U is the Fourier transform of the
undriven (passive) position data, and .omega.=2.pi.f, where f is
the frequency.
At process step 110, the trapped bead is oscillated relative to the
sample and along a plane transverse to the path of the detection
beam. In some embodiments, the bead can be oscillated relative to
the sample by oscillating the trap beam using an acousto-optic
deflector (AOD) when the sample remains stationary. In other
embodiments, the bead can be oscillated relative to the sample by
oscillating a nanopositioning stage (such as a piezo stage) holding
the sample when the trap beam remains stationary.
The trap beam (or stage) can be oscillated with a complex waveform
comprising a predetermined combination of frequencies. In some
embodiments, the complex waveform used to oscillate the bead
comprises a combination of frequencies (for example, from 10-50
frequencies, such as from 10-30 frequencies, from 10-20
frequencies, from 15-25 frequencies, or 10, 15, 20, 25, 30, 35, 40,
45, or 50 frequencies) that are selected to provide distinct
harmonics and reduce cross talk, and to cover a frequency range
that can provides sufficient data for determination of the trap
stiffness. For example, the complex waveform used to oscillate the
bead comprises a combination of prime frequencies (for example,
from 10-50 prime frequencies, such as from 10-30 frequencies, from
10-20 prime frequencies, from 15-25 prime frequencies, or 10, 15,
20, 25, 30, 35, 40, 45, or 50 prime frequencies). In some
embodiments, the complex waveform used to oscillate the bead
comprises a combination of frequencies that are a predetermined
multiple (such as 10.times., 50.times., 100.times., or 200.times.)
of prime frequencies that are selected to provide distinct
harmonics and reduce cross talk, and to cover a frequency range
that can provides sufficient data for determination of the trap
stiffness. In some embodiments, the combination of frequencies can
comprise or consist of frequencies (such as prime frequencies) of
from 3 to 101 Hz, from 3 to 157 Hz, from 3 to 997 Hz, from 2 to 101
Hz, from 2 to 157 Hz, from 2 to 997 Hz, from 1 to 10 Hz, from 1 to
1000 Hz, from 1 to 10000 Hz, from 1 to 20000 Hz, from 100 to 1000
Hz, from 100 to 10000 Hz, from 100 to 20000 Hz, from 300 to 1000
Hz, from 300 to 10000 Hz, from 300 to 20000 Hz, from 1000 to 10000
Hz, or from 1000 to 20000 Hz, for example. In some embodiments, 2
sets of twenty multiplexed frequencies, ranging from 3-101 and 300
to 15700 Hz, can be obtained, and the high frequency data can be
used to calibrate the trap (due to lower noise present at high
frequencies in the power spectrum, trap calibration was much more
accurate at the higher frequencies).
In some embodiments, to ensure that the amplitude of the resulting
multiplexed waveform results in a maximum displacement of the probe
that remains within the linear range of both the trap and detection
beams, the component sines of the combination of frequencies in the
complex waveform are given phase offsets. For example, the
frequencies can be offset in phase by 0.degree., 45.degree.,
-45.degree., and -90.degree.. The effect of the phase offsets is to
reduce the stacking of the peaks of (especially the lower)
frequencies so the bead does not exceed a linear range of
viscoelasticity of the biological material. In some embodiments,
oscillating the trapped bead relative to the sample comprises
oscillations of no more than 200 nm from the bead's equilibrium
position.
In some embodiments, oscillation amplitude per frequency and laser
power can both be modified to alter the level of stress/strain
applied to the sample. Laser powers can be varied between 10-500 mW
(measured immediately before entry into the rear port of the
microscope), as needed. In some embodiments, laser oscillation
amplitudes can be varied between 1-100 nm to ensure the optical
trap and trapped bead remain in the linear regime of detection beam
and trapping laser.
In addition to multiplexed frequency measurement, measurements at
single frequencies (1, 10, 100, 1000, 10000 Hz), with oscillation
amplitudes of 1, 10, or 100 nm, and/or laser powers of 10, 50, 100
or 500 mW can be used.
In some embodiments, the trap beam (or sample stage) is first
actively oscillated, followed by a passive phase in which the trap
is held stationary at the bead's equilibrium position. In
non-limiting embodiments, the measurements can be acquired with 1 s
(1/2 s active, 1/2 s passive) pulses for a set number of seconds
(such as 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 20, 30, or 60 seconds) at
an appropriate acquisition rate such as 80 kHz, or 2-s pulses (1 s
passive, 1 s active) for a set number of seconds (such as 1, 2, 3,
4, 5, 6, 7, 8, 9, 10, 20, 30, or 60 seconds) at an appropriate
acquisition rate, such as 20 kHz. During the active pulse, the trap
position is oscillated by a multiplexed waveform consisting of the
sum of sines spanning a broad band of frequencies. After the trap
is displaced according to the waveform, the probe motion is
recorded with trap stationary during the passive pulse.
In some embodiments, the trap position is oscillated to drive bead
displacement, and the active power spectrum {tilde over
(R)}.sub.L(.omega.) is recorded as:
.function..omega..function..omega..times..times..omega..times..times..fun-
ction..omega..times..times. ##EQU00001## where {tilde over
(x)}.sub.dr(.omega.) and {tilde over (x)}.sub.L(.omega.) are
Fourier transforms of the driven bead and trapping laser positions,
respectively. Note that {tilde over (x)}.sub.dr(.omega.) and {tilde
over (x)}.sub.L(.omega.) are complex, accounting for the relative
phase of the trap and bead oscillations.
Based on the measurements of passive and active movement of the
bead, the trap stiffness can be calculated, for example, using
equation (3):
.kappa..omega..times..function..omega..function..omega..times..times.
##EQU00002## where Re indicates the real component and
k.sub..omega. is the trap stiffness at .omega.. The trap stiffness
is typically constant over all oscillation frequencies as long at
the bead is oscillated in a linear range of viscoelasticity of the
sample. The friction relaxation spectrum can then be obtained with
equation (4):
.gamma..function..omega..times..times..omega..times..times..kappa..omega.-
.times..times..omega..times..times..times..omega..times..times..function..-
omega..times..times. ##EQU00003## and the complex modulus can be
derived from the relaxation spectrum for spherical probes of a
known radius R by equation (5):
.function..omega..times..times..omega..times..times..gamma..times..omega.-
.times..times..pi..times..times..times..times. ##EQU00004##
In some embodiments, the disclosed systems and methods can utilize
automated programming, allowing the selection of multiple probe
sites at once, to increase throughput. In addition, further
automation (automated probe selection), and efficient selection of
necessary experimental variables can be used to reduce assay
time.
In some embodiments, the disclosed systems and methods can assay
viscoelastic properties of a sample, such as a biological material,
with a broad dynamic range of movement and force applied to an
optical trap bead (such as from 1-10000 Hz, 1-10000 s Pa, and/or
1-200 nm), and can resolve changes in the local rheology on the
order of 10 s of microns and 10 s of microseconds scale. By
actively probing at a wide range of frequencies (1-20,000 Hz),
amplitudes (1-200 nm) and trap powers (1-500 mW), it is possible to
measure the properties of the sample microenvironment surrounding
the trapped bead on different time, length, and force scales. The
disclosed systems and methods can also be used to measure the local
rheological anisotropy by oscillating in more than one
dimension.
In some embodiments, the movement and force applied to an optical
trap bead can have a frequency of from 1-20,000 Hz, such as from
1-20,000 Hz, from 10-20,000 Hz, from 100-20,000 Hz, from
1000-20,000 Hz, from 1-15,000 Hz, from 10-15,000 Hz, from
100-15,000 Hz, from 1000-15,000 Hz, from 1-10,000 Hz, from
10-10,000 Hz, from 100-10,000 Hz, or from 1000-10,000 Hz.
In some embodiments, the movement and force applied to an optical
trap bead can have an optical trap force of from 1-10000 Pa, such
as from 1-100 Pa, from 10-10000 Pa, from 100-10000 Pa, from
1000-10000 Pa, from 1-1000 Pa, from 10-1000 Pa, from 100-1000 Pa,
from 1-5000 Pa, from 10-5000 Pa, from 100-5000 Pa, or from
1000-5000 Pa.
In some embodiments, the movement and force applied to an optical
trap bead can have an amplitude of movement of from 1 to 200 nm,
such as from 1-10 nm, from 1-100 nm, from 1-20 nm, from 1-50 nm,
from 10-50 nm, or from 100-200, or from 50-200 nm.
In some embodiments, the force applied to an optical trap bead can
be applied with a trap power of from 1-500 mW, such as from 1-100
mW, from 5-100 mW, from 10-100 mW, from 50-100 mW, from 5-500 mW,
from 10-500 mW, from 50-500 mW, from 100-500 mW, or from 1-10 mW,
or 1 mW, 10 mW, 50 mW, 100 mW, 200 mW, or 500 mW.
In cases where the assayed sample is optically transparent, for
example 3D tissue cultures and in vivo tissues, a forward
scattering optical trap system can be used. For samples that are
not optically transparent, a backward scattering optical trap
system can be used.
The disclosed methods and systems can also be used in the diagnosis
and/or treatment of a particular condition or disease associated
with tissue/cell remodeling, including tumor state. The disclosed
methods and/or systems can be used to determine the effectiveness
of a particular compound or treatment regimen for altering the
viscoelastic properties of a sample, such as a tissue (for example
skin or tumor tissue). For example, the present methods and systems
can be utilized to determine the effectiveness of cosmetic
products, such as the effectiveness of products for reducing
wrinkles and scarring of skin. In some examples, the disclosed
methods and systems are used to evaluate wound healing, such as to
determine the effectiveness of a treatment for wound healing,
including, but not limited to, wound healing in a diabetic
patient.
In some embodiments, the disclosed systems and methods can be used
to interrogate the viscoelastic properties of a tumor and/or the
tumor microenvironment. During metastasis, tumor cells encounter
new microenvironments. First, they adhere and remodel the host
organ to proliferate and form a new neoplasm, or a new tumor organ.
Tumor cells receive both chemical and physical cues from the
surrounding stromal cells and the extracellular matrix within this
dynamic milieu. Preliminary studies have indicated that physical
properties involving stiffness, dimension and topography strongly
influence cell fate and malignancy (Gauvin and Khademhosseini
(2011) Acs Nano 5(6): 4258-4264; Kumar and Weaver (2009) Cancer
Metast Rev 28(1-2): 113-127; Yang et al., (2005) Biomaterials
26(15): 2603-2610). In particular, the physical properties of the
local (microscale) environment, such as the forces that cells
experience, influence gene expression, cell signaling, and motility
(Wang et al., (2009) Nat Rev Mol Cell Bio 10(1): 75-82). These data
indicate that microscale mechanical heterogeneities are major
factors in cancer outcome.
In several embodiments, the disclosed systems and methods can be
used to interrogate the rheological properties of tumors and/or the
tumor microenvironment. For example, such assays can be performed
before any after application of a test agent to determine if it
alters the tumor or the tumor microenvironment. A tumor is an
abnormal growth of tissue or cells that results from excessive cell
division. A tumor that does not metastasize is referred to as
"benign." A tumor that invades the surrounding tissue or can
metastasize (or both) is referred to as "malignant." The tumor
microenvironment is the cellular environment in which a tumor
exists, including surrounding blood vessels, immune cells,
fibroblasts, signaling molecules, and the extracellular matrix
(ECM), including stromal cells. Tumors can influence the
microenvironment by releasing extracellular signals, promoting
pathological angiogenesis and inducing peripheral immune tolerance,
while the immune cells in the microenvironment can affect the
growth and evolution of cancerous cells. In some embodiments, the
disclosed systems and methods can be used to assay the viscoelastic
properties of mechanical fibrosis in clinically relevant samples,
such as ductal carcinomas with fibrotic focus, which are more
likely to recur and metastasize.
Non-limiting examples of tumors and/or tumor microenvironments that
can be assayed include the following tumor types as well as their
microenvironment: sarcomas (connective tissue cancer) and
carcinomas (epithelial cell cancer), including fibrosarcoma,
myxosarcoma, liposarcoma, chondrosarcoma, osteogenic sarcoma, and
other sarcomas, synovioma, mesothelioma, Ewing's tumor,
leiomyosarcoma, rhabdomyosarcoma, colorectal carcinoma, lymphoid
malignancy, pancreatic cancer, breast cancer, lung cancers, ovarian
cancer, prostate cancer, hepatocellular carcinoma, squamous cell
carcinoma, basal cell carcinoma, adenocarcinoma, sweat gland
carcinoma, medullary thyroid carcinoma, papillary thyroid
carcinoma, pheochromocytomas sebaceous gland carcinoma, papillary
carcinoma, papillary adenocarcinomas, medullary carcinoma,
bronchogenic carcinoma, renal cell carcinoma, hepatoma, bile duct
carcinoma, choriocarcinoma, Wilms' tumor, cervical cancer,
testicular tumor, seminoma, bladder carcinoma, and CNS tumors (such
as a glioma, astrocytoma, medulloblastoma, craniopharyogioma,
ependymoma, pinealoma, hemangioblastoma, acoustic neuroma,
oligodendroglioma, menangioma, melanoma, neuroblastoma and
retinoblastoma).
As used in this application and in the claims, the singular forms
"a," "an," and "the" include the plural forms unless the context
clearly dictates otherwise. Additionally, the term "includes" means
"comprises." Further, the term "coupled" does not exclude the
presence of intermediate elements between the coupled items.
The systems, apparatus, and methods described herein should not be
construed as limiting in any way. Instead, the present disclosure
is directed toward all novel and non-obvious features and aspects
of the various disclosed embodiments, alone and in various
combinations and sub-combinations with one another. The disclosed
systems, methods, and apparatus are not limited to any specific
aspect or feature or combinations thereof, nor do the disclosed
systems, methods, and apparatus require that any one or more
specific advantages be present or problems be solved. Any theories
of operation are to facilitate explanation, but the disclosed
systems, methods, and apparatus are not limited to such theories of
operation.
Although the operations of some of the disclosed methods are
described in a particular, sequential order for convenient
presentation, it should be understood that this manner of
description encompasses rearrangement, unless a particular ordering
is required by specific language set forth below. For example,
operations described sequentially may in some cases be rearranged
or performed concurrently. Moreover, for the sake of simplicity,
the attached figures may not show the various ways in which the
disclosed systems, methods, and apparatus can be used in
conjunction with other systems, methods, and apparatus.
Additionally, the description sometimes uses terms like "produce"
and "provide" to describe the disclosed methods. These terms are
high-level abstractions of the actual operations that are
performed. The actual operations that correspond to these terms
will vary depending on the particular implementation and are
readily discernible by one of ordinary skill in the art.
In some examples, values, procedures, or apparatus' are referred to
as "lowest," "best," "minimum," or the like. It will be appreciated
that such descriptions are intended to indicate that a selection
among many used functional alternatives can be made, and such
selections need not be better, smaller, or otherwise preferable to
other selections.
EXAMPLES
The following example is provided to illustrate particular features
of certain embodiments, but the scope of the claims should not be
limited to those features exemplified.
Example 1
In Situ Calibrated Mechanical Properties of Tissue Microenvironment
In Vivo
The example provides an active microrheology optical trapping
method for analysis of the viscoelastic properties of heterogeneous
biological materials, such as in vivo samples. In the disclosed
method, optical trap beads are calibrated in situ to obtain trap
stiffness to quantify local applied forces. Applicable to multiple
sample types, including thick tissue, this method allows
quantitation of mechanical heterogeneities with micrometer spatial
resolution at penetration depths up to 500 mm, such as in living
zebrafish. Microscale differential stresses and strains were
applied over a broad range of frequencies to measure the mechanical
response of distinct organs to reveal the frequency dependent
viscoelasticity on time, length, and force scales relevant to
protein-protein interactions, cytoskeletal remodeling, molecular
motor activity, in addition to slower processes such as 3D cell
motility, cell proliferation and the establishment of multicellular
structures.
Materials and Methods
Sample Preparation--Microrheology
ECM Hydrogels.
Matrigel (Corning (#354230, Lot #3032578)) and Hyaluronan (ESI BIO
(Hystem #GS311)) were stored at 4.degree. C. until use. Gels were
polymerized as previously described (Blehm, et al., Biomaterials 56
(2015) 129e139; Tanner et al., PNAS, 109 (6) (2012) 1973e1978).
Briefly, carboxylate modified red fluorescent beads (Life
Technologies Fluorospheres, F8887) .about.1 mm in diameter were
first sonicated for 45 min immediately before use. Fluorescence
excitation of the beads was 546 nm. These monodisperse beads were
then uniformly mixed into either the liquid Matrigel or Hyaluronan
at a density of 5.times.108 beads/mL chilled on ice. 450 ml of this
bead-ECM mixture was directly pipetted into a Willco Well dish
(WillCo Wells, GWSB5040), and allowed to polymerize in an incubator
at 37.degree. C. for 90 min. Cell media was then added to the well,
and the dish was returned to the incubator until used. The
measurements are performed in an aqueous environment at room
temperature.
Zebrafish.
The transgenic zebrafish line Tg(kdrl:GFP)la116), which stably
expresses EGFP in the vasculature, was used. Zebrafish were
maintained at 28.5.degree. C. on a 14-h light/10-h dark cycle
according to standard procedures. Embryos were obtained from
natural spawning and raised at 28.5.degree. C. and maintained in
egg water containing 0.6 g sea salt per liter of DI water. Embryos
were injected at the single cell stage with 2 nL of bead/sterile
PBS solution of 5.times.108 beads/mL of monodisperse
carboxylate-modified red fluorescent beads. Between 10 and 16 h
post fertilization (hpf), embryos were transferred to eggwater
supplemented with phenylthiourea (PTU, Sigma P5272), suspended at
7.5% w/v in DMSO, at 1 part in 4500 to inhibit melanin formation
and increase optical transparency. Embryos were then returned to
the incubator at 28.5.degree. C. and checked for normal development
and widely dispersed beads daily using fluorescence microscopy.
Mechanical characterization was performed 72 h post fertilization
(72 hpf). Zebrafish embryos were anesthetized using 0.4% buffered
tricaine, then embedded in a lateral orientation in 1% low melting
point agarose (NuSieve GTG agarose, Lonza), and allowed to
polymerize on a 50 mm glass bottom dish with cover glass no. 1.5
thickness. Egg water supplemented with tricaine was added to the
agarose hydrogel for the entire time of data acquisition and used
as the immersion medium. The maximum time of data acquisition on
each embryo did not exceed 4 h. Fish were fixed in 4%
paraformaldehyde solution for 2 h and then prepared for
histological staining Briefly, fish were embedded in Optimal
Cutting Temperature compound (OCT) prior to frozen sectioning on a
microtome-cryostat. Serial sections 8 microns thick were labeled
for specific stains as delineated by Masson trichrome, modified
Movat and Haematoxylin and eosin. Briefly, the slides were hydrated
and then stained with hematoxylin and eosin. They were then
dehydrated and cleared and cover slipped, resulting in nuclei
stained blue and cytoplasm pink. For M. trichrome, the slides were
hydrated, then mordant in bouin to stain slides in Weigert
hematoxylin followed by biebrich scarlet/Acid fuchsin combo. The
slides were then placed in a combination of phosphomolybdic and
phosphotungstic acid. Finally, they were stained with aniline blue
and then hydrated and cleared. The slides were mounted with
permount. Collagen stains blue and muscle red. For Movat after
hydration, slides were stained with verhoeffs hematoxylin, followed
by treatment with 2% ferric chloride. The slides were then placed
in 5% hypo solution and stained in 1% alcian blue, then with a
combination of crocein scarlet and acid fuchsin. They were then
rinsed in 0.5% acetic acid and finally stained with alcoholic
saffron solution. Nuclei stain black, cytoplasm red, collagen
yellow, elastic fibers black and muscles stain red.
Optical Trap.
A simplified schematic of the instrument is shown in FIG. 3. The
optical trap is comprised of two lasers, one that traps and one
that detects. The light path of the trapping laser originates from
non-polarized light emitted by an IPG Photonics 1064 nm laser
(#YLR20-1064-Y11). This beam is then linearly polarized by placing
a polarizing beam splitter cube (Thorlabs PBS23) into the light
path. Beam power is either manually controlled by adjusting a
half-wave plate (WPH05M-1064) or controlled by changing the input
voltage of the power supply of the trap laser. For the latter,
manipulation is achieved using an analog channel of a DAQ card
(#PCIe-5871R FPGA DAQ, National Instruments), or manually on the
touchscreen of the power supply. This adjusted beam is then
directed through another beam splitter cube. Trap steering at the
sample plane is achieved by using a 2D Acousto-Optic Deflector
(AOD) from IntraAction (DTD274HD6), which is conjugated to the back
focal plane. The AOD is driven by radio frequency (RF) generating
cards (Analog Devices #AD9854/PCBZ), which are controlled by the
digital outputs of the data acquisition (DAQ) card (#PCIe-5871R
FPGA DAQ, National Instruments). A second half-wave plate is used
to direct the correctly polarized beam into the AOD. The AOD mount
(New Focus 9081, Newport) is used to adjust the beam's entrance
angle to ensure maximal diffraction into the doubly diffracted
first-order beams. This customized adjustable AOD mount required
machining a coupling plate to attach the AOD. An iris is used to
isolate the doubly diffracted first-order diffracted beam. This
beam is then directed into the objective with two lens telescopes
(100 mm and 200 mm, and 50 mm and 125 mm, LA1509-C, AC508200-B,
LA1131-C, LA1384-C respectively, Thorlabs). A third half-wave plate
in the beam path allows for polarization adjustments to the beam
before it enters the microscope. A beam pick (BSF10-C, Thorlabs) is
used to separate .about.1 percent of the beam, which was attenuated
with a ND Filter (NENIR210B, Thorlabs), and directed to the trap
QPD (QP154-Q-HVSD, First Sensor), to determine the oscillation
phase of the trap laser. An iris is once again used to isolate only
the doubly diffracted first-order diffracted beam.
Spatial distortion in the beam profile is introduced when the
trapping beam is diffracted by the AOD. The detection beam removes
this noise. The detection laser was a 975 nm Lumics diode
(#LU0975M00-1002F10D) cased in a Thorlabs mount (LM1452, TED200C,
DC210C). This laser can only be operated at a very high power
(>10 mW). Hence, the power was attenuated by first passing the
beam through a neutral density (ND) filter (NENIR220B, Thorlabs)
reducing the power to <1 mW. Alignment of the attenuated
detection beam with the trapping laser beam was achieved by
manipulation of a broadband dielectric mirror (BB1EO3IR, Thorlabs)
and a dichroic mirror (T1020LPXR, Chroma). The trapping beam enters
the objective (MRDO7602 CFI-PLAN-APO VC60XA WI 1.2NA, Nikon),
slightly overfilling its back aperture (the detection beam is much
smaller). Both beams are sent into the objective by reflection off
a filter cube (ZT1064rdc-2p dichroic, Chroma). The two beams are
then collected by a water condenser (WI 0.9NA, Nikon), before being
decoupled from the microscope light path by a dichroic mirror
(ZT1064RDC-2P, Chroma) that was attached to the microscope using
custom machining The trapping beam is then filtered using an
emission filter (ET980/20X, Chroma). A First Sensor Quadrant
PhotoDiode (QPD) (QP154-Q-HVSD) is used to determine the position
of the detection beam and the sum, left-right difference, and
top-bottom difference channel voltage readouts are obtained by
analog input channels of the DAQ card.
The microscope stage is controlled by both a motorized stage (X-Y-Z
axes) (Prior #77011201) and a piezo stage (X-Y-Z axes) (Mad City
Labs #77046501). Images were acquired with an ANDOR Ixon real gain
camera (DU-897E-C50-#BV). Bright field illumination was achieved
using a Prior LED light source (LDB101-NI). The supplemental
mirrors and irises shown in the schematic not specifically detailed
above were all obtained from Thorlabs (part numbers: BB1-E03IR,
BB2-E03IR, ID25). The shutter is from Uniblitz (VS1452Z0R3) and the
base microscope is a Nikon Eclipse Ti-U. Data acquisition and laser
control were achieved using custom Labview programs.
Power Supply and Other Electronics.
Electronics used in the setup were driven by Acopian power
supplies: A50MT100 (QPD bias voltage), TD15-40 (QPD power),
A24H1500 (amplifier power), and A3.3NT350 (RF card power). The RF
cards for the AOD had onboard 60 MHz crystal oscillators (Anodyne
Components, ZKG10A1N-60.000M) multiplied 5.times. onboard to give a
reference clock of 300 MHz. The RF signal was then amplified
(Minicircuits, ZHL-1-2 W-S) and DC blocked (Minicircuits,
BLK-89-S). All RF cable connections were comprised of triply
shielded cables (Minicircuits, cb1-10FT-SMSM) to reduce noise. All
electronics were powered by filtered AC that had been first passed
through a Back-UPS Pro1000, and then an isobar ultra.
Microrheology
Calibration of Laser Alignment.
A optical trap built around a modified Nikon Eclipse TieU
microscope base was used for all trapping measurements. Before each
experiment, the trap was calibrated for alignment and functionality
using a control sample of carboxylated beads in PBS at a
concentration of 107 beads per mL. Briefly, the calibration
involves trapping a bead, which is then oscillated using the AOD at
magnitudes that can be easily observed on the CCD camera (typically
equivalent to 500 nm). The trap's oscillation is detected on the
trap QPD, and then the detection laser's response is verified on
the detection QPD. Maximum response to oscillations in both
dimensions (x and y), while ensuring oscillation in either
dimension is also decoupled from the other dimension, is found by
adjusting the detection laser mirror and dichroic mirror. This
signal is then centered in the middle of the range where its
response is optimal. The detection QPD is then adjusted such that
the detection beam is centrally located in both x and y. Once this
is accomplished, the trap is calibrated in water using the power
spectrum method (see, e.g., Visscher et al., Nature 400 (6740)
(1999) 184e189, which is incorporated by reference herein in its
entirety) and then calibrated using the active-passive method
described herein. Finally, the bead position on the CCD is
determined by centroid-fitting an image of the bead on the camera,
and this position is used as the trap position in the
trap-centering algorithm.
Data Acquisition.
Samples are loaded on the microscope stage. Typically, an image of
512.times.512 square pixels is recorded by the CCD camera, and then
beads that are in focus at a given plane are manually selected. The
software records the positions of each of these beads and the
active oscillation is performed systematically, where the data
acquisition proceeds bead by bead. For each bead, an image of a
subset of the original area encompassing 21.times.21 square pixels
is acquired for each bead's position, and then the centroid is
estimated to determine the bead's center. The trap laser is then
centered to that bead's location by the piezo stage. A 49-image z
stack comprised of images 100 nm apart is acquired, and the center
of the bead in the axial direction (z axis) is determined by
detection of the maximum bead intensity. With the trap laser off, a
volt to nanometer conversion calibration for each bead is
calculated by stepping the piezo stage in X and Y (10 nm per step,
11 steps) through the bead. The detection QPD's voltage is recorded
and normalized to the sum of the total voltage on the QPD for each
dimension (x and y). A high NA condenser collects all scattered
light from the bead and the conjugate image of the bead is mapped
onto the back-focal plane and collected on the QPD (Farre &
Montes-usategui, 2010; Gittes & Schmidt, 1998; Grange, Husale,
Guntherodt, & Hegner, 2002; June, Tripathy, Narayanareddy,
Mattson-hoss, & Gross, 2014). A line fit to the data is used to
obtain a volt to nanometer conversion in both dimensions (x and y).
Example volt to nanometer calibrations performed in zebrafish are
shown in FIG. 9. An additional check can be performed to ensure
that this conversion is correct. For example, if the measurements
are not linear where the R2 is <0.95, the entire dataset for
that bead can be discarded. The volt to nanometer conversion is
usually the major source of noise when calibrating the bead
displacement for optically heterogeneous samples.
In Situ Calibration.
In OT-based microrheology, small refractive probes are embedded in
tissue to serve as local microenvironment sensors (FIG. 4A). When a
laser beam focuses on a bead, refraction-induced changes in the
momentum of light produce a harmonic potential within the laser's
focal volume, trapping the bead in a force field such that it
undergoes spring-like oscillations about the trap center if
perturbed by an applied force, where the displacement amplitude
.DELTA.x is related by F=-k.DELTA.x to the perturbing force F by
the trap stiffness k. In passive microrheology, mechanical
properties of the bead's local microenvironment are determined from
thermal forces due to Brownian motion; in active microrheology, the
trapping laser's position is oscillated to apply forces. Accurate
deduction of these forces by direct measurement of bead
displacements requires that k is known. In prior optical trap
methods, k is typically estimated before an experiment by
calibration in a known viscous material, assumed to have the same
refractive index n as the sample. This approach is inapplicable in
vivo, since tissues are optically heterogeneous and the refractive
indices are unknown a priori.
Starting from this framework, three measurements are obtained to
calibrate the trap stiffness. To determine in situ calibration of
each measured bead, three steps were performed: 1) detector
sensitivity calibration, 2) detection of a trapped particle's
(passive) thermal motion, and 3) detection of its (active) motion
in response to force applied by oscillating the trap position.
First, the change in volts per nanometer of bead displacement,
.beta., is found for the detection QPD by piezo-stepping the bead
through the detection laser beam. Second, the thermal power
spectrum of the bead's motion P.sub.U (.omega.) is recorded:
P.sub.U(.omega.)={tilde over (x)}.sub.U(.omega.)|.sup.2, equation
(1) where {tilde over (x)}.sub.U is the Fourier transform of the
undriven (passive) position data, and .omega.=2.pi.f, where f is
the frequency. Third, the trap position is oscillated to drive bead
displacement, and the active power spectrum {tilde over
(R)}.sub.L(.omega.) is recorded:
.function..omega..function..omega..times..times..omega..times..times..fun-
ction..omega..times..times. ##EQU00005## where {tilde over
(x)}.sub.dr(.omega.) and {tilde over (x)}.sub.L(.omega.) are
Fourier transforms of the driven bead and trapping laser positions,
respectively. Note that {tilde over (x)}.sub.dr(.omega.) and {tilde
over (x)}.sub.L(.omega.) are complex, accounting for the relative
phase of the trap and bead oscillations. Finally, the trap
stiffness is found:
.kappa..omega..times..function..omega..function..omega..times..times.
##EQU00006## where Re indicates the real component and
k.sub..omega. is the trap stiffness at .omega.. The trap stiffness
should be constant over all frequencies. This allows measurement of
both the trap stiffness in viscoelastic material and the local
environment's complex shear modulus. As force is actively applied,
this is an active microrheological technique. The friction
relaxation spectrum can then be obtained with equation (4):
.gamma..function..omega..times..times..omega..times..times..kappa..omega.-
.times..times..omega..times..times..times..omega..times..times..function..-
omega..times..times. ##EQU00007## and the complex modulus can be
derived from the relaxation spectrum for spherical probes of a
known radius R by equation (5):
.function..omega..times..times..omega..times..times..gamma..times..omega.-
.times..times..pi..times..times..times..times. ##EQU00008##
The complex modulus was measured at two sets of twenty multiplexed
frequencies, one ranging from 3 to 101 and another from 300 to
15700 Hz. These sets of frequencies were primes (chosen to evenly
cover the range of interest), or 100.times. a set of primes, to
ensure distinct harmonics and prevent cross talk between
frequencies. The amplitude of each component sine was equal. Thus,
for the measurements, the trap is first actively oscillated,
followed by a passive phase in which the trap is held stationary at
the bead's equilibrium position. Although use of a complex waveform
introduces noise, the multiplexing allows the frequencies to be
recorded simultaneously, reducing measurement times. During the
active pulse, the trap position is oscillated by a multiplexed
waveform consisting of the sum of sines spanning a broad band of
frequencies. After the trap is displaced according to the waveform,
the probe motion is recorded with trap stationary during the
passive pulse. To ensure that the amplitude of the resulting
multiplexed waveform results in a maximum displacement of the probe
that remains within the linear range of both the trap and detection
beams, the component sines are given phase offsets. The frequencies
were offset in phase by 0.degree., 45.degree., -45.degree., and
-90.degree.. The effect of the phase offsets is to reduce the
stacking of the peaks of (especially the lower) frequencies so the
probe is never moved more than 200 nm from its equilibrium
position. Hence, all measurements were performed in the linear
regime of the trapping and detection lasers. High frequency
multiplexed data (>300 Hz) was acquired with 1 s (1/2 s active,
1/2 s passive) pulses for seven seconds, at an acquisition rate of
80 kHz. These data were then used to calibrate the trap, as the
noise is minimal at higher frequencies in the passive spectrum,
leading to more accuracy at the higher frequencies. Low frequency
multiplexed data (<300 Hz) was acquired with 2-s pulses (1 s
passive, 1 s active) for 20 s at an acquisition rate of 20 kHz.
Other Calibration Techniques Using the Power Spectrum to Obtain
V-nm Calibration.
After trapping a bead in water, position data is acquired for 7
half-second pulses at 40 kHz. During this time the trap is
oscillated at 500 Hz, with 50 nm amplitude. After this data is
acquired, it is Fourier transformed into the frequency domain, and
the power spectral density (PSD) of the data is taken for each
pulse and then averaged over the pulses. This PSD is then fit with
the equation:
.function..pi..function..times..times..delta..function..times..times.
##EQU00009## where P(f) is the PSD, D is the diffusion coefficient,
f is the frequency, f.sub.c is the critical frequency, and
f.sub.drive is the frequency at which the trap is oscillating.
After fitting, the volts-to-nanometers calibration for the detector
and the trap stiffness can be determined from the fitted
parameters. First, the volts-to-nanometers conversion is determined
by the theoretical work (W.sub.th, nm) in the oscillation peak
divided by the experimentally measured work (W.sub.ex,V) in the
oscillation peak,
.beta..times..times. ##EQU00010## where .beta. is measured in nm/V,
and
.times..times..times. ##EQU00011## while
W.sub.ex=(P.sup.volts(f.sub.drive)-P.sub.T.sup.volts(f.sub.drive)).DELTA.-
f, equation (9) Here P.sup.volts(f.sub.drive) is the PSD in volts
at f.sub.drive, and P.sub.T.sup.volts(f.sub.drive) is the thermal
background at f.sub.drive. Then the trap stiffness can be
determined using the equation:
.times..times..pi..times..times..times..kappa..times..beta..times..times.-
.times. ##EQU00012##
where k.sub.ex is the trap stiffness, k.sub.B is the Boltzman
constant, T is the absolute temperature, and D.sup.volt is the
diffusion coefficient measured in volts.
Bulk Rheology.
All bulk rheology measurements were carried out using an Anton Paar
Physica MCR 301 rheometer equipped with a PP-25 measuring plate
(parallel, 25 mm diameter). HA and Matrigel hydrogel samples were
prepared by pipetting 450 ml of bead-ECM solution (stock Matrigel
or pre-mixed HyStem chilled on ice) on Willco wells (GWSB-5040)
containing a steel washer (1 mm thick, 25 mm inner diameter), and
spreading the solution to fill the washer. The samples were then
incubated at 37.degree. C., in 5% CO2 for 90 min. 3 mL of PBS was
added to the samples and they were incubated overnight. The next
day, PBS was aspirated immediately before measurement. First, the
top parallel plate was lowered to contact the surface of each
sample until a load of 0.2 N was achieved. Frequency sweeps (0.1e10
Hz, 5 points per decade) were then conducted at three strains
(0.1%, 1%, 10%). Finally, an amplitude sweep (0.1%-30%) at constant
frequency (1 Hz) was performed to confirm that measurements were
acquired in the linear range of viscoelastic deformation.
Measurements were carried out in triplicate. The measurements are
performed in an aqueous environment at room temperature.
Confocal Microscopy.
Images other than those captured on the trap were confocal images
acquired using a Zeiss 780 LSM, using Zen software for data
acquisition. Living zebrafish embryos were anesthetized using 0.4%
buffered tricaine and then embedded in a lateral orientation in 1%
low melting point agarose (NuSieve GTG agarose, Lonza). Live cell
imaging was performed on zebrafish mounted in 4 or 8-well plates
for time-lapse imaging to monitor development. Z stacks were
acquired using a tiled approach and a 10.times. air objective of
0.3 NA where each individual image comprised 2046.times.2046 square
pixels corresponding to 1416.times.1416 square microns for a total
z distance of 276 microns. One Z stack was taken every 20 min from
the time of injection to ensure regular development. Images of
zebrafish probed on the trap were also taken, to determine the bead
distribution in the entire fish.
Results
AMOTIV and Bulk Rheology Measure Similar Values for Amorphous
Hydrogels.
The relationship between microscale mechanical properties compared
to bulk properties in materials of known extracellular matrix (ECM)
composition and architecture was assayed using our optical set-up
(see schematic shown in FIG. 4A). To avoid microscale
heterogeneities, the complex shear moduli
(G*(.omega.)=G'(.omega.)+iG''(.omega.), with G'(.omega.) and G''
the storage and loss moduli, respectively) of uniform amorphous
hydrogels, Matrigel and HA, was first measured (FIG. 4B). The
measurements for the storage moduli agree quite closely with small
angle oscillatory shear (SAOS) bulk rheology measurements in their
common low frequency range, with elastic plateaus from .about.10 to
100 Hz (Matrigel: G'.sub.10-100 HZ=47.+-.4 Pa, G''.sub.10-100
HZ=10.+-.3 Pa, HA: G'.sub.10-100 HZ=27.+-.2 Pa, G''.sub.10-100
HZ=7.+-.2 Pa) (FIG. 4B). Using the optical trap, it was possible to
probe at higher frequencies than those attainable by bulk rheology.
At higher frequencies, both hydrogels display weak power-law
frequency dependence in G' .varies. .omega..sup..alpha. and G'
.varies. .omega..sup..beta. (Matrigel: .alpha..about.0.31,
.beta..about.0.59; HA: .alpha..about.0.34, .beta..about.0.72),
increasing monotonically (Matrigel: G'.sub.15kKz.about.185.+-.82
Pa, G''.sub.15kKz.about.214.+-.11 Pa; HA:
G'.sub.15kKz.about.107.+-.21 Pa, G''.sub.15kKz.about.159.+-.4.5 Pa)
with G''>G' at crossover frequencies of 9.5 kHz (Matrigel) and 5
kHz (HA).
Characterization of Tissue ECM In Vivo.
Next microscale zebrafish tissue mechanics were assayed. At the
single cell stage embryo, carboxylated beads are injected and
dispersed throughout the animal as the embryo develops. A
widespread distribution of beads was observed. Some beads lie
within the brain cavity as well as stuck along blood vessel walls
throughout the brain, trunk and tail of the animal. Only beads that
are fixed to the blood vessel wall were assayed, to probe the ECM
lining of the vessels. Standard histological stains were also
performed to show the distribution of common ECM proteins such as
collagens, mucins and fibrins to show the complexity of the tissue
microenvironment in the fish.
In Situ Calibration of Optical Trap Stiffness Accurately Resolved
Tissue Heterogeneities In Vivo.
The optical setup was used to probe tissue mechanical properties in
vivo by actively applying force to a bead, and then converting the
bead's response relative to the driving force into the local
viscoelasticity. One important step is the ability to calibrate
trap stiffness accurately for each probe. In situ calibration was
compared with other commonly used methods, some of which assume
hydrogel and tissue samples have refractive indices similar to
water, and that calibration of .beta. and .kappa..sub..omega. in
water is sufficient for monodisperse beads in hydrogels and living
zebrafish (FIG. 5). As can be seen in FIG. 5, previously used
methods all lead to significant overestimation of the complex
moduli, with high frequency linear fits showing significantly large
differences in slope (p<0.01). This discrepancy could be due to
the fact that beads in viscoelastic samples do not freely fall into
the center of the trap as they do in water, which is important
since .beta. and .kappa..sub..omega. vary along the beam axis.
These issues were avoided by placing the trap on the bead center
(found by centroid fitting the bead's Gaussian intensity profile).
Additionally, the sample refractive index, n, may differ
significantly from that of water. Hence, OT is calibrated in a
viscous material with a similar n to that of the sample. This
approach ignores any heterogeneity in bead size, trap properties
due to differential scattering, and tissue refractive index. To
perform this calibration, the .kappa..sub..omega. of each bead
measured in situ (.kappa..sub..omega.,bead) was averaged
(.kappa..sub..omega.) and .kappa..sub..omega. was used to calculate
G*(.omega.). In both thick hydrogels and distinct tissues of
zebrafish larvae (brain and tail), the complex moduli calculated
from .kappa..sub..omega. were significantly (p<0.01 when
comparing the high frequency linear fits) greater (approximately
two fold) than those calculated from .kappa..sub..omega.,bead
measured individually (FIGS. 5 and 6).
The discrepancy between methods was then determined by calculating
the overestimation factor of G' or G'' at each frequency relative
to our method (G.sub.calibration(.omega.)/G.sub.InSitu(.omega.)),
and then averaging over frequency to determine an average
overestimation for each method. Using the corresponding
.kappa..sub..omega. water, .beta. water, or .kappa..sub..omega.
average to obtain the moduli leads to significant (p<0.0001 when
comparing the normalized average values between calibrations)
overestimation, up to 20-fold (FIGS. 5 and 6). Although averaging
over each probe's trap stiffness in the sample gave superior
results to the water calibrations, ignoring spatial heterogeneities
still led to overestimation of the complex modulus.
Nonlinear Microrheology in 3D Hydrogels and Zebrafish.
Biological materials often show stress-strain dependent
viscoelastic response. Accordingly, the in vitro microscale
stress-strain behavior was compared to the bulk properties to
determine if non-linear behavior existed at the microscale that was
not observed in the same material under macroscale examination.
Stress-strain behavior in bulk rheology were obtained by varying
the applied strain and performing frequency sweeps (0.1-10 Hz, 5
points per decade) at each strain (e.g. 0.1%, 1%, 10%). For an
optical trap, there are two ways to vary the stress and strain
applied to the probe's microenvironment: 1) by changing the trap
position oscillation amplitude or 2) by changing the laser power
(FIG. 7A). Since the applied force F and the displacement of the
bead from the trap center .DELTA.x are related to the trap
stiffness k by F=-k.DELTA.x, altering the oscillation amplitude or
trap stiffness changes both the stress and strain applied to the
gel. A greater frequency dependence of storage and loss moduli in
Matrigel and HA acquired was observed at lower trap powers and
lower oscillation amplitudes (FIG. 8). Interestingly, power law
exponents fit to high frequency (>500 Hz) HA data cluster around
0.7 for the loss moduli, similar to what would be expected for
semi-flexible polymer networks. However, in Matrigel, exponents
cluster around 0.6, closer to the exponent expected for a flexible
polymer network. Both Matrigel and HA elastic moduli display power
law exponents <0.5, (Matrigel: 0.31-0.38; HA: 0.3-0.48). The
power law exponent of the viscous moduli did not significantly
depend on the trap power or oscillation amplitude in either
material, but the elastic moduli in HA did significantly depend on
trap power (p<0.0001), indicating nonlinear, stress-strain
dependent behavior occurs in HA. In contrast, stress strain
behavior measured by bulk rheology in HA and Matrigel mostly
display constant elastic and viscous moduli at different strains,
even though there are divergences even at low frequencies in the
microrheology data (FIG. 7).
3D culture models are used to mimic the chemical and mechanical
properties and dimension of in vivo tissue architecture. However,
in vivo tissues may show variations in mechanical properties, not
only due to spatial heterogeneities, but non-linear behaviors that
amorphous 3D ECM models fail to display. Additional assayed were
performed to determine if tissues display behaviors similar to
those observed in 3D hydrogels similar to known polymer theories.
Comparison of microscale stress-strain behavior at varying trap
powers and amplitudes in the zebrafish display regime-dependent
polymer dynamics (FIG. 8) where power law exponents fitted at high
frequencies (>500 Hz) ranged 0.5-0.8. Interestingly, at trap
power of 10 mW, the tail and brain of the zebrafish have loss
moduli power law exponents of 0.76 and 0.66 (.about.semi-flexible),
while at 100 mW, they are 0.44 and 0.5 (approaching flexible
behavior). Similarly, the elastic moduli of the tail and brain at
10 mW have loss moduli power law exponents of 0.63 and 0.73,
respectively, compared to 0.5 and 0.48 at 100 mW (FIG. 8). In
zebrafish, over half of the power law exponent fits show
significant trap power dependence (p<0.01), as opposed to
hydrogels, where only the HA's elastic moduli showed such a
dependence. This indicates significantly that more non-linear
behavior exists in living tissue than is present in 3D culture
models.
Discussion
To test the validity of the in situ calibration disclosed herein,
it was reasoned that amorphous, uniform hydrogels would enable the
most direct comparison between bulk rheology and microrheology.
Comparable values were observed for the storage loss moduli using
both the microscale and bulk techniques. However, there was
approximately an order of magnitude difference between the micro
and bulk measurements (FIG. 4). A non-limiting explanation for this
finding is that it may be due to microdomains that affect the local
viscosity that may not be resolvable in the bulk measurements.
Knowing the trap stiffness (and thus the applied force) for each
probe enables interrogation of the mechanical response to force as
a function of stress and strain amplitude within thick hydrogels
and in vivo. In situ calibration at each probe was shown to improve
accuracy, and temporal and spatial resolution sufficiently to
resolve in vivo tissue heterogeneities. Previous studies to
characterize in vivo tissue dynamics in animal models such as
zebrafish (Danio rerio), fruit flies (Drosophila Melanogaster), and
nematodes (Caenorhabditis elegans) have largely relied on
measurements based on passive microrheology due to thermal
fluctuations. Specifically, the passive cytoplasmic characteristics
of zebrafish and other embryos have been discussed, but the precise
and absolute rheological properties of the tissue microenvironment
have not been previously attained. Here the first in vivo
characterization of zebrafish tissue rheology is provided.
The multiplexed waveform to modulate the trapping laser's position
was comprised of a sum of sines at multiple frequencies, which
reduces time for data acquisition. Prime numbers can be used for
the input sine waves as the higher order harmonics of prime
frequencies do not overlap, thus reducing crosstalk between
frequencies during active oscillations. In particular, the waveform
of the trap position was a linear combination of the twenty
frequencies with equal amplitudes. The measurement was broken into
two separate waveforms of 20 multiplexed frequencies because of the
concern of leaving the linear regime of the viscoelastic response,
as well as the linear response of the QPD. As a consequence, the
maximum total displacement from the equilibrium position of the
bead did not exceed 200 nm. As such, all measurements at all
frequencies were conducted in the linear regime. Strictly speaking,
the bead is simultaneously experiencing oscillations at each
multiplexed frequency, and therefore as its displacement varies
throughout the course of the waveform, it is the case that the trap
displacement is equal for each frequency. The bead displacement at
each frequency is variable, and is part of the measurement. It
would not be possible to a priori know the bead displacement given
a specific trap displacement prior to the measurement, as the
bead's response to the trap is what is being measured. The subtlety
here is that with this type of multiplexing, the perturbation
occurring at each frequency can be viewed as having a fixed
amplitude but with a varying amount of prestress, which is a
function of the composite waveform. However, the average prestress
is zero. The phase offsets of 0, 45, -45, and -90 degrees are used
to reduce the maximum displacement of the trap so that the bead
never leaves the linear regime of the trapping or detection laser
beams. This is increasingly evident at lower frequencies, where if
the same phase is used for all frequencies the peaks would "stack"
to a greater degree in the multiplexed waveform. When there were no
phase offsets, then there will be cross talk at higher
harmonics.
In light of the fact that application of prestress can indeed alter
the mechanical response in comparison to a non-prestressed
situation, before undertaking this approach we performed
comparisons between the shear moduli resulting from multiplexed
measurements and standard single-frequency measurements in the same
samples. Exemplary data is provided in FIGS. 10 and 11. While the
results are not indistinguishable, it is believed that that in the
context of the aggregate measurement error, the increase in
statistical power gained by increased sample size due to reduction
in measurement times attributable to multiplexing outweighed the
discrepancy due to the introduction of this prestress.
Using the disclosed optical trap system and method it was possible
to probe a greater dynamic range (frequencies spanning from 1 Hz to
15 kHz) than those probed using most bulk rheological instruments.
This range covers time scales that are relevant for understanding
the effect of the microenvironment on faster processes such as
protein-protein interactions, cytoskeletal remodeling, molecular
motor activity (which in turn affects slower processes such as 3D
cell motility), cell proliferation and the establishment of
multicellular structures.
The disclosed optical trap apparatus and method was compared with
other methods, which assume hydrogel and tissue samples have
refractive indices similar to water or lack heterogeneity, and that
calibration of .beta. and .kappa..sub..omega. in water is
sufficient or that an average calibration could be applied to the
entire sample. These other methods led to significant
overestimation of the complex moduli (FIGS. 5 and 6).
Microscale stress strain behavior in uniform amorphous hydrogel
also showed differences as a function of applied stress that were
not observed at overlapping frequencies of bulk rheological
measurements. These data reinforce the need to examine different
spatial, temporal and force regimes to fully assess the effects on
tissue behavior. Also, it was demonstrated that in vivo tissue
mechanical properties are distinct from those seen in ECM hydrogels
as determined by microscale stress strain behavior. In particular,
living tissue's mechanical response is more stress dependent than
3D hydrogels, as at low stress it displayed behavior similar to
semiflexible polymers, while at higher stresses behaved similar to
flexible polymers. The differences measured at different trap
powers and oscillation amplitudes indicate that we may be probing a
different regime of mechanical behavior than the bulk measurement,
likely due to the fact that our microrheological measurements
subject a small region of the sample to stress much greater than
that applied by bulk rheometers which distribute the stress over
the entire sample.
One consideration when varying laser power is the effect of
localized heating as the power is increased. In The disclosed
optical trap system and method, the 1064 nm CW laser induced
heating, which results in .about.8 K/W heating at the focus, based
on previous studies. Thus, laser power of 100 mW corresponds to
.about.0.8 K. At higher powers this begins to matter more,
especially in the effect on the power spectrum, which is obtained
by applying a Lorentzian fit to determine the trap stiffness.
Additionally, heating may also reduce the fluid viscosity, but this
will depend on the material and the effects on protein matrix or
tissue are even less established for obvious reasons. These effects
can be seen as laser powers are increased to 500 mW as shown in
FIG. 10.
The optical tap beads used in this example were 1 .mu.m
carboxylated microspheres, and did not freely diffuse in any of the
samples on the assayed experimental time-scales, indicating that
they are larger than the local microenvironment's mesh size.
Therefore the disclosed methods assay the protein polymer mesh that
makes up the local ECM microenvironment of the cell, and not only
the surrounding fluid phase.
Example 2
In Situ Calibrated Mechanical Properties of Ex Vivo Tumor
Microenvironment
This example illustrates use of the optical trap method and system
disclosed in Example 1 to obtain microrheological data from tumor
samples ex vivo. It was found that mouse melanoma tumors and human
breast tumors displayed complex moduli .about.5-1000 Pa, increasing
with frequency and displaying a nonlinear stress-strain response.
Direct calibration of trap stiffness at each probe allows the
determination of absolute forces needed to resolve local
heterogeneities in tumor samples. Thus, the disclosed microrheology
methods can be used to provide a mechanical biopsy as a diagnostic
tool to aid in design of therapeutics that would be complementary
to those based on standard histopathology.
Materials and Methods
Microsphere PEGylation.
Fluorescent 1 .mu.m carboxylated polystyrene spheres conjugated to
Rhodamine (Thermofisher #8821) were centrifuged and resuspended in
10% molar excess EDC
(1-ethyl-3-(3-dimethylaminopropyl)-carbodiimide) for 1 h. The beads
were centrifuged and resuspended in 50.times. molar excess ethylene
diamine for 6 h and agitated on a shaker at medium speed overnight.
Beads were then centrifuged and resuspended in a solution
containing 2.times. molar excess mPEG-SVA adjusted to pH 8 with
NaOH overnight, then agitated on a shaker overnight. Beads were
centrifuged and resuspended in deionized water.
Ex Vivo Tumors
Cell Lines.
Tumor cell lines, a mouse melanoma cell line, B16F10 (cat. No.
CRL-6475) and a human breast adenocarcinoma cell line, MDA-MB-231
(cat. No. HTB-26) were obtained from American Type Culture
Collection (ATCC, VA). Briefly, both cell lines were cultured as
monolayers in DMEM high glucose media (Life technologies, CA)
supplemented with final volume of 10% Fetal Bovine Serum (FBS), 1%
MEM non-essential amino acids, L-glutamine, penicillin and
streptomycin. Medium was refreshed every 2-3 days.
Lentiviral Transduction.
Cells were transduced with virus using the ExpressMag Transduction
System (Sigma). Briefly, viral supernatant was incubated with
magnetic beads at room temperature for 15 min, added to the
adherent cells and placed on a strong magnetic plate at 37.degree.
C. for 12 min. Media was replenished 16 hr. later and the viral
mixture disposed of in compliance with NIH policy. Transduced cells
were selected with 2 .mu.g/ml puromyocin (InvivoGen, San Diego,
Calif.). Flow cytometry was performed to isolate the GFP/luciferase
positive cells from cells that did not the express these markers
using the Cell Sorting feature on a BDFACS Aria (BD
Biosciences).
In Vitro Bioluminescence Activity Assay.
Luciferase activity of pre-sorted cells was determined using
VivoGlo.TM. luciferin (Promega, Madison, Wis.), according to the
manufacturer's instructions. Briefly, 1.times.10.sup.4 of
GFP/Luciferase and its parental cells were seeded on a white-walled
96-well plate (Corning, Corning, N.Y.). Cells were washed with PBS
and then mixed with 150 .mu.l/ml of luciferin in IMDM media
(Gibco). After 10 minutes, luciferase activity was measured by
Infinit200.RTM. Pro Luminometer (Tecan, San Jose, Calif.). For each
experiment, 3 individual samples were prepared.
Tumor Injections.
Briefly, a cell and fluorescent bead suspension in PBS was injected
subcutaneously in the flanks of 8-10 week old female nu/nu mice
where the final cell number was 5.times.10.sup.5 cells and 10.sup.7
beads. Tumor burden was estimated by weekly physical and in vivo
bioluminescence measurements and mice were euthanized as tumors
approached 1 cm in diameter with no detectable metastasis, as
determined from BLI imaging. Luminescence emitted by tumors in nude
mice was measured weekly. Briefly, each mouse was injected
intra-peritoneally with 100 .mu.l of VivoGlo.TM. luciferin at 3
mg/ml in PBS. Mice were imaged on the dorsal and ventral sides and
the luciferase signals were captured by a Xenogen IVIS-200 system
(Perkin-Elmer, Waltham, Mass.). The luminescence quantity was
displayed by radiance and the units are displayed as
photons/s/cm.sup.2/sr.
Ex Vivo Tumor Preparation.
Fresh tumors were excised and half of the sample was prepared for
ex vivo imaging and the other for histological analysis. Half of
the tumor was immediately placed in 4% paraformaldehyde solution
for 12 h and then prepared for histological staining Tumors were
then embedded in paraffin prior to sectioning on a microtome.
Serial sections, 8 .mu.m thick were labeled for specific ECM stains
as delineated by Masson trichrome, and Haematoxylin and eosin as
previously described (Blehm et al., 2015). The second half was then
thinly sliced and mounted on a No. 0 Willco glass bottom dish to
perform mechanical measurements.
Optical Trap-based Microrheology was performed as described in
Example 1.
Results
The complex moduli of the tumors was measured using the disclosed
optical trap based active microrheology. To confirm similar stages
of tumor progression for each sample, the absence of distant
metastasis was confirmed using bioluminescent imaging (BLI) and
visual examination of organs at necropsy. B16-F10 melanoma tumors
exhibited a nonlinear mechanical response; storage moduli differed
significantly (p<0.004) with oscillation amplitude (2 nm, 5 nm,
10 nm, 20 nm). Complex moduli (G*) exhibited weak power law
frequency dependence with power law exponents of 0.70, 0.63, 0.57,
and 0.52 at amplitudes 2 nm, 5 nm, 10 nm, and 20 nm, respectively.
Storage and loss moduli rise monotonically 5 Pa-1000 Pa over
frequencies 3 Hz-15 kHz, (FIG. 12). MDA-MB-231 breast tumor samples
had similar mechanical properties (FIG. 12).
Discussion
The active microrheology measurements described here of the murine
tumor microenvironment are the first of their kind. Fluorescent
beads and fluorescence microscopy were used to avoid inadvertent
measurement of vesicles and other small round objects in the tumor.
Such objects can be trapped and measured, but careful consideration
of their surface moieties and size is needed to determine accurate
displacement-viscoelasticity conversions.
Atomic force microscopy (AFM) has been used to assess the elastic
modulus of individual collagen fibers and collagen rich tumor
stroma ex vivo. AFM micro- and nano-indentation gives a higher
spatial resolution compared to bulk rheological methods, allowing
examination of individual fibers and/or superficial mechanical
mapping of tissues. Elegant studies have shown that an increase in
Young's modulus is indicative of the malignant transformation
during human breast tumor progression with the largest value at the
invasive front. Plodinec and co-workers conducted AFM indentation
measurements with sharp tips on human breast tumors measured at
frequencies .about.0.8-1 Hz, finding a trimodal distribution of
Young's moduli with peaks at .about.1, 2, and 6 kPa (Plodinec,
Loparic, Monnier, Obermann, Zanetti-Dallenbach, Oertle, Hyotyla,
Aebi, Bentires-Alj, H., et al., 2012). AFM indentation measurements
on human breast tumors measured at 20 .mu.m/s with a 5 .mu.m
spherical probe showed Young's moduli .about.1 kPa (Acerbi et al.,
2015). Interestingly mouse melanoma cell and human breast cancer
cell tumors measured herein were as much as two orders of magnitude
softer at comparable frequencies. It was determined that mouse
melanoma tumors also exhibited nonlinear stress-strain behavior,
with frequency dependence shifting from semi-flexible to flexible
behavior with increasing stress-strain amplitude, as obtained for
collagen hydrogels. In addition, it was determined that mouse
melanoma tumors and human breast tumors displayed elastic moduli
.about.5 to .about.1000 Pa, increasing monotonically with
frequency. Mouse melanoma tumor samples also exhibited nonlinear
stress-strain behavior in the tumor, with frequency dependence
shifting from semi-flexible to flexible behavior with increasing
stress-strain amplitude.
Example 3
In Situ Calibration of Position Detection in an Optical Trap for
Active Microrheology in Viscous Materials
In optical trapping, accurate determination of forces requires
calibration of the position sensitivity relating displacements to
the detector readout via the V-nm conversion factor (.beta.).
Inaccuracies in measured trap stiffness (k) and dependent
calculations of forces and material properties occur if .beta. is
assumed to be constant in optically heterogeneous materials such as
tissue, necessitating calibration at each probe. For solid-like
samples in which probes are securely positioned, this can be
achieved by moving the sample with a nanopositioning stage and
stepping the probe through the detection beam. However, in many
samples a different method is needed. Here, we introduce a simple
method to find .beta. in any material by steering the detection
laser beam while the probe is trapped. We demonstrate the approach
in the yolk of living Danio rerio (zebrafish) embryos and measure
the viscoelastic properties over an order of magnitude of
stress-strain amplitude.
As disclosed herein optical trapping can be applied in
three-dimensional (3D) tissue microenvironments in vivo to
interrogate viscoelastic response over a broad range of
frequencies, and can be used to probe stress-strain behavior by
modulating the forces on the trapped particle (active
microrheology), which is of interest since many biomaterials and
specimens exhibit nonlinear viscoelasticity. Accurate determination
of these forces requires knowledge of the optical trap stiffness,
k, and the probe's displacement from equilibrium, .DELTA.x.
Determining .DELTA.x can be accomplished by calibrating the
position sensitivity, 1/.beta., of the detector, which relates the
detector readout (in volt) to the probe's displacement (in
nanometer). Measuring forces in biological materials including
tissues is non-trivial because both k and .beta. vary from probe to
probe throughout the sample due to intrinsic optical and mechanical
heterogeneities.
FIG. 13A depicts an microrheology measurement scheme employing
active-passive calibration described in Examples 1 and 2, in which
mechanical properties of viscoelastic samples are determined from
the thermal power spectrum and the active power spectrum (obtained
by oscillating the trap position). An advantage of this approach is
that the optical trap stiffness, k, is determined in situ from the
spectra of each probe. However, .beta. is not given by the spectra
and requires an additional measurement for samples like the
optically heterogeneous tissues of the zebrafish embryo (FIG. 13B).
This example provides additional methodology for determining .beta.
in viscous materials.
A common and effective way to measure probe displacements in
optical traps is by back focal plane interferometry (See, e.g.,
Denk and Webb, Appl. Opt., 29(16) 2382-2391 (1990); and Allersma et
al., Biophys. J., 74(2) 1074-1085 (1998), each of which is
incorporated by reference herein). When a probe of diameter d is
trapped at the center of the beam waist of a laser with wavelength
.lamda. focused by an objective in its image plane, some light
undergoes scattering due to light-probe interactions and (in the
dipole limit d<.lamda.) produces spherical waves. This scattered
light slightly diverges from the fraction of light that does not
undergo scattering. Thus, shifts in relative phase between these
two wavefronts give rise to a pattern of constructive and
destructive interference. A high numerical aperture (NA) condenser
collects this light, and is placed in Kohler illumination such that
the image planes of the field diaphragm iris and the objective are
conjugate and image into each other (forming a Keplerian
telescope). Behind the condenser, a dichroic mirror reflects the
detection beam (but not the trap beam or lamp light) onto a
detection lens that is positioned to relay the image at the back
focal plane of the condenser onto a QPD. In this configuration,
displacements of the probe cause rotation of the detection beam in
the image plane and corresponding translations of the beam at both
the back-aperture of the condenser and on the detection QPD. The
interference pattern is mapped onto the QPD; so lateral
displacements of the probe relative to the detection beam in the
imaged plane result in changes in voltage. The voltage response
.DELTA.S is linearly related to probe translations for small
displacements (.DELTA.x.+-..about.150 nm from the probe center).
Thus, calibrating the position detection sensitivity consists in
finding the V-nm relation .DELTA.x=.beta..DELTA.S.sub.x in the
linear response regime.
A number of methods may be used to calibrate .beta., each
applicable in various situations (FIG. 13C). When the temperature
and the Brownian dynamics of the probe and material are known,
methods based on recording the thermal power spectrum are
frequently used, but are generally inapplicable to microrheology
since they depend on independent knowledge of the dynamic viscosity
or related frictional terms (FIG. 13C (1)). Additionally,
biomaterials may exhibit glassy dynamics and are out of thermal
equilibrium. In another method, the trap is moved rapidly while the
impulse response of the QPD is tracked as the probe relaxes to its
new position, but this too relies on the drag coefficient. In
materials where a priori knowledge of the physical properties of
the tissue is not known, determination of .beta. requires other
methods. Tolie-Norrelykke et al. demonstrated that by imposing a
known oscillating flow in combination with the power spectrum
method, both the drag coefficient and .beta. can be determined
(Tolie-Norrelykke, et al., Rev. Sci. Instrum., 77(10), 2006). This
approach requires that the induced motion in the liquid be
synchronized with an imposed low frequency stage oscillation (an
AOD oscillation would also work), which may not be the case in
biphasic materials, and will not work in samples that show
nonlinearities or elastic effects. A direct method is to scan the
probe across the waste of the detection beam by employing a
piezoelectric nanopositioning system (NPS) to step the sample stage
with known displacements (Allersma et al., Biophys. J., 74(2)
1074-1085, 1998). This `piezo method` requires calibration of the
NPS, which can be accomplished by imaging displaced probes with a
camera of known pixel size (FIG. 13C (2)). This method works in
nonlinear or elastic materials where the probe motions are confined
and remain correlated to the stage displacements, including some
tissues with fine meshwork. However this is not the case in more
fluid-like environments, wherein yet other methods must be
used.
This example provides beam steering approach, but uses a weak
secondary detection beam to scan across the probe while it is
confined in the trap (FIG. 13C (3)). This method is therefore
applicable to probes that are either weakly attached to or freely
moving through the microenvironment, such as in the perivascular
microenvironment in the zebrafish trunk depicted in FIG. 13B. It
also works for probes that are strongly attached or confined in a
solid-like microenvironment, and the microenvironment may be
nonlinear, viscous, elastic or viscoelastic with unknown Brownian
dynamics. The method produces independent measurements of .beta. in
good agreement with the power spectrum method and the piezo
scanning method.
Optical Trap
The optical trap setup is depicted in FIG. 14. A trapping beam and
a detection beam are each steered with dual axis AODs, where the
(1-1) diffracted (1st order in both dimensions) beam is selected
with an iris. Prior to experiments, the Hz-nm relations of the AODs
are calibrated by attenuating and focusing the beam on a coverslip
and imaging the backscattered beam on a CCD camera. To detect trap
displacement, the beam is split with a beam sampler mirror directly
after the acousto-optic deflector (AOD) to direct a small amount of
power onto the `trap` QPD. This QPD is not in a conjugate plane, so
changes in QPD voltage are correlated to beam displacements. A high
numerical aperture (NA), long working distance (WD) condenser that
collects all light from the objective. Behind the condenser, a
dichroic mirror decouples the trap beam and lamp light from the
detection beam which is sent through a relay lens that is
positioned to image the back focal plane of the condenser onto the
detection QPD. Time-correlated trap and probe QPD signals are
recorded on a FPGA (field programmable gate array) DAQ (data
acquisition) card, which also controls TCXO (temperature controlled
crystal oscillator)-generated radio frequency (RF) signals that
drive the AODs. Control and data collection are conducted in custom
LabVIEW programs.
Before each experiment, beams are aligned and tested using a
control sample of carboxylated beads in water. First the trapping
beam is oscillated and centered on the trap QPD by adjusting the
relay mirror between the trap QPD and the beam sampler mirror. Next
a bead is trapped, the trap is oscillated, and the detection beam
is co-aligned with the trapping beam by adjusting the dichroic
mirror that couples the trapping and detection beams. Oscillation
and adjustment is conducted iteratively in each lateral dimension.
Finally, the detection QPD is adjusted so the signal from a trapped
bead in equilibrium falls on its center. After beam alignment the
thermal power spectrum is recorded (blocking with eight separate
measurements) while the trap is oscillated at 500 Hz with amplitude
of 50 nm. The viscosity and .beta. are calculated from the spectrum
by fitting to a Lorentzian to ensure that the measured viscosity of
water is accurate and that the positional sensitivity is consistent
with previous values specific to the setup and alignment of the
microscope. Finally, the bead position on a charge-coupled device
(CCD) camera is determined by centroid-fitting an image of the bead
on the camera, and this position is used as the lateral trap
position.
With the beams aligned, measurements are then conducted in the
sample material. A probe is selected and brought to the lateral
trap position by moving the piezo stage. With the objective focus
in the specimen plane, the condenser is adjusted to Kohler
illumination. The probe is then axially centered in the trap by
stepping the objective vertically through 49 steps, recording a
bright field image with the CCD camera at each step, and moving the
probe to the plane with the highest intensity image. The stage,
trap, and probe are held stationary, and the detection beam
position is oscillated sinusoidally at a frequency f.sub.drive of 1
kHz with a displacement amplitude of 54.7 nm for a measurement time
t.sub.msr of 1 s across the center of the probe while the detection
QPD voltages are recorded at a sampling rate of 80 kHz. The
resulting voltage time series are then Fourier transformed into the
frequency domain with a frequency bandwidth .DELTA.f of 1 Hz,
giving a voltage frequency spectrum, which exhibits a strong peak
at f.sub.drive. Because the drive period (1 ms) divides evenly into
t.sub.msr, the peak is a single datum rather than having finite
width. The voltage at f.sub.drive is then divided into the
displacement amplitude of the detection beam to give .beta. in
nmV.sup.-1. The process can be conducted consecutively in each
dimension.
Following .beta. calibration, a set of measurements are conducted
to give both k and the complex modulus and complex viscosity of the
microenvironment as a function of the stress-strain amplitude (A,
in nm displacement) and frequency (.omega.) at which the trap is
oscillated, G*(.DELTA., .omega.) and .eta.*(.DELTA., .omega.),
respectively. The measurements consist of separate recordings of
the power spectra of the probe during passive motion (during which
the trap is stationary) and active motion (during which the trap is
oscillated over a range of frequencies) to get the active and
passive power spectra substantially as described in Example 1. In
active measurements, the trap was displaced by a waveform
consisting of the superposition of 20 sine waves of equal amplitude
at frequencies ranging 2 Hz-12,863 Hz (a set of logarithmically
distributed prime numbers to ensure distinct harmonics. The
frequencies were alternately offset in phase by 0.degree.,
45.degree., -45.degree., and -90.degree. to minimize the maximum
trap displacement, which was 200 nm, within the linear regime of
the trapping and detection lasers. Each probe was subject to 7
sequential pulses, where each pulse consisted of 2 s active motion
followed by 2 s passive motion. In all samples, only probes at
distances exceeding .about.30 .mu.m away from the cover slip
surface were measured to minimize drag in consideration of Faxen's
law.
Animal Studies.
Wildtype and transgenic (Tg(fli-1:eGFP)/Tg(gata-/:dsRed)) zebrafish
(Danio rerio) were maintained at 28.5.degree. C. on a 14 h light/10
h dark cycle according to standard procedures. Embryos were
obtained from natural spawning and raised at 28.5.degree. C. and
maintained in egg water containing 0.6 g sea salt per liter of DI
water. 2 nL of monodisperse of 1 .mu.m rhodamine carboxylated
fluospheres (Thermofisher #F8821) at 5.times.10.sup.8 beads/mL in
sterile PBS was microinjected into the zebrafish embryo yolk.
Between 10 and 16 h post fertilization (hpf), embryos were
transferred to egg water supplemented with phenylthiourea (PTU,
Sigma P5272), suspended at 7.5% w/v in DMSO, at 1 part in 4500 to
inhibit melanin formation and increase optical transparency.
Embryos were then returned to the incubator at 28.5.degree. C. and
checked for normal development and widely dispersed beads daily
using fluorescence microscopy. Mechanical characterization was
performed 48 h post fertilization (hpf). Zebrafish embryos were
anesthetized using 0.4% buffered tricaine, then embedded in a
lateral orientation in 1% low melting point agarose (NuSieve GTG
agarose, Lonza), and allowed to polymerize on a 50 mm glass-bottom
dish with cover glass no. 1.5 thickness. Egg water supplemented
with tricaine was added to the agarose hydrogel for the entire time
of data acquisition and used as the immersion medium. The maximum
time of data acquisition on each embryo did not exceed 4 h.
Silicone Solutions.
Polydimethyl siloxane (PDMS) (Dow Corning Sylgard 184 silicone
elastomer base) was combined with Sylgard 184 silicone curing agent
at a 10:1 ratio in a weighing boat on a digital scale. 20 .mu.l of
bead/sterile PBS solution of 5.times.10.sup.8 beads/mL of
monodisperse 1 .mu.m rhodamine carboxylated fluospheres
(Thermofisher #F8821) was added during 10 min of thorough mixing
with a pipette tip. A flow chamber was made using two strips of
double sided scotch tape, a No. 1.5 cover slip and a microscope
slide. With vacuum pressure applied to one end of the chamber a
small volume of the solution was pulled in from the other end so no
air bubbles remained. Samples were measured immediately and only
within 30 min of initial mixing. Basement membrane ECM hydrogels
(Matrigel (Corning (#354230, Lot #3032578))) were prepared as
described in Example 1. Rat tail collagen I hydrogels (BD
Biosciences, San Jose, Calif., USA) were prepared as previously
described (see, Artym and K. Matsumoto, Curr Protoc Cell Biol.,
10-18 (2010); Staunton et al., Sci. Rep., 6, 19686, 2016).
Results
FIG. 15 shows example data comparing .beta. calibrations by the
piezo stage stepping and detection beam steering methods of a probe
injected into a zebrafish embryo located in a solid-like region of
the tail (FIG. 15A, FIG. 15C) and another probe in a fluid-like
region of the yolk (FIG. 15B, FIG. 15D). During piezo calibration,
the probe in the tail was confined and moved in tandem with the
piezo stage (FIG. 15A). The resulting QPD signal, in V, in the
dimension parallel to the stage movement is plotted against the
position in nm. .beta. is determined simply by fitting a line in
the central, linear response region (.+-..about.150 nm from the
probe center). Multiple samples of the voltage are averaged before
fitting to reduce noise. This is performed in each lateral
dimension. The piezo calibration fails for unconfined probes. The
resulting signal for the probe in the yolk was very noisy, which
possibly moved completely out of the detection beam path (FIG.
15B). To overcome this limitation, the detection beam steering
(FFT) method was employed. The method works both for confined
probes (FIG. 15C, zebrafish tail) or unconfined probes (FIG. 15D,
zebrafish yolk). Noise present at low frequencies is avoided by
oscillating at a single high frequency. Signal-to-noise ratio can
be improved by increasing the collection time, or by averaging a
number of separate measurements. In cases where the piezo method is
applicable, FFT and piezo results agree well. For confined 1 .mu.m
diameter carboxylated polystyrene microspheres embedded in rat-tail
type I collagen hydrogels (2 mgml.sup.-1 initial concentration;
polymerized at 37.degree. C.), both methods were used to calculate
(FIG. 16A). The ratio of the two values was taken for each probe,
with a value of 1.04.+-.0.09 (Gaussian fit parameters,
mean.+-.standard deviation), a discrepancy falling below the range
of other sources of error. In cases where the thermal power
spectrum (PSD) method is applicable, the FFT method produces
results in agreement with the PSD method. The values of .beta.
determined by the FFT and PSD methods were compared for probes in
water and in surrogate basement membrane extracellular matrix
hydrogels, assuming the drag coefficient of water in both cases. As
expected, the PSD method cannot be used in elastic or viscoelastic
materials such as reconstituted surrogate basement membrane
extracellular matrix hydrogels, as the drag coefficient is
incorrect and the spectrum does not fit a Lorentzian function. When
calculated under these inappropriate conditions, values for .beta.
were found to be as much as nearly 100-fold greater than those
calculated for the same probes by the FFT method. However, in water
(FIG. 16B), the two methods produce remarkably similar values. The
PSD method resulted in values 1% greater on average than the FFT
method, with a standard deviation under 4%.
Uncured polydimethylsiloxane (PDMS) was next used as a phantom to
test the FFT method in a viscous fluid. For each probe, .beta. and
k was calibrated in situ and multiplexed frequency sweeps (2
Hz-12.9 kHz) were performed at stress-strain amplitudes of 2 nm, 5
nm, and 20 nm (trap position displacements) per frequency. FIG. 17
shows the resulting elastic (G') (FIG. 17A) and viscous (G'') (FIG.
17B) components and magnitude (G*) of the complex shear modulus
(FIG. 17C). Uncured PDMS exhibited nonlinear viscoelasticity, with
moduli increasing approximately one order of magnitude with an
order of magnitude increase in applied stress-strain amplitude
across the frequency range (two-way ANOVA, p<0.0001). The onset
of shear thinning occurred at a critical shear rate of .about.500
Hz. At 2 Hz, the corresponding complex viscosity .eta.* was
approximately 25 Pas, 35 Pas, and 450 Pas at 2 nm, 5 nm, and 20 nm,
respectively.
Active microrheology measurements were then performed on the yolks
of anaesthetized zebrafish embryos 48 h post fertilization. In
order to probe the nonlinear stress-strain response, the trap
position was oscillated at stress-strain amplitudes of 2 nm, 5 nm,
10 nm, and 20 nm per frequency. FIG. 17 shows the resulting elastic
(G') (FIG. 17D) and viscous (G'') (FIG. 17E) components and
magnitude (G*) of the complex shear modulus (FIG. 17F). The moduli
increase significantly with increased applied stress across the
frequency range (two-way ANOVA, p<0.0001). G' increased from
.about.2 Hz-750 Hz, decreasingly slightly with frequency
thereafter. At stress-strain amplitudes of 20 nm, G' rose from 20
Pa-200 Pa, falling again to 35 Pa. The amplitude had greater effect
at lower frequencies. G' at 20 nm amplitudes was .about.40-fold
greater than 2 nm amplitudes at 2 Hz, while only .about.4-fold
greater at 12.9 kHz. G* increased from 2 Hz-1 kHz, leveling off at
higher frequencies. The effect of stress-strain amplitude on G''
varied less frequency, with G'' at 20 nm amplitudes .about.2-3-fold
greater than at 2 nm amplitudes. At 20 nm, G'' rose from .about.2
Pa-100 Pa. The corresponding complex viscosity .eta.* decreased
from .about.5 Pas-0.01 Pas at 20 nm and .about.1 Pas 0.006 Pas at 2
nm.
Discussion
In optical trap methods where the sample material properties are
unknown and cannot be assumed, some form of direct measurement of
the V-nm conversion factor must be conducted. Many materials of
interest are both biphasic and feature heterogeneous microdomains
of various sizes such that, among a population of monodisperse
probes, some are firmly enmeshed or caged by fibers or other
solid-phase material, others are free to diffuse, and the remainder
are in an intermediate regime of partial confinement. The piezo
stage-stepping method for in situ position detection calibration
may not be applicable under these circumstances. Furthermore,
nonlinear and elastic effects may be present, ruling out many other
methods.
This example provides an alternative method to find the V-nm
conversion factor of a probe that can be used in liquid or
liquid-like material with nonlinear viscoelastic effects, using AOD
beam steering of the secondary detection laser across the trapped
probe center. The method gives results in good agreement with the
power spectrum density and piezo stage stepping methods, and
expands the range of materials in which in situ calibration is
possible. One caveat is that if the underlying structure of the
material influences the detection beam over the length scale of its
displacement, then there may be some systematic noise associated
with the displacement of the detection beam. This is also true of
the piezo method and back focal plane interferometry generally,
since it is sensitive not only to scattering by the probe but also
to other objects in the beam path. As the detection beam is moved
during this calibration process, it may be modulated by scattering
from local optical inhomogeneities that introduce a potential
source of uncertainty. This possibility was examined by measuring
the signal on the detection QPD while oscillating the detection
beam in the absence of a trapped probe at a number of random
locations. Across the length scale of the oscillation the signals
were found to be indistinguishable.
The optical trap method for active microrheology was then applied
in the yolks of zebrafish embryos 48 h post fertilization. Physical
properties like cell stiffness, viscosity and cortical tension are
critical to cell migration, adhesion and division in during
embryonic development. Various reports of avian egg viscosity range
from 10.sup.-2 Pas-1 Pas, which is the same range our measurements
fall within. Example 1 illustrated measurement of the extracellular
matrix viscoelasticity in vivo in zebrafish brain and tail tissue,
finding G' and G'' rising from .about.1 Pa-1 kPa over the frequency
range 3 Hz-15 kHz. The example illustrated that the yolk presents
similar behavior up to several hundred Hz, but in contrast to the
brain and tail tissues, the moduli in the yolk feature a plateau at
.about.100 Pa from .about.750 Hz-12.9 kHz, corresponding to the
onset of increased shear thinning The yolk exhibited nonlinear
stress-strain response, with as much as 40-fold increase in G' at
low frequencies in response to a 10-fold increase in stress-strain
amplitude.
It will be apparent that the precise details of the methods or
compositions described may be varied or modified without departing
from the spirit of the described embodiments. We claim all such
modifications and variations that fall within the scope and spirit
of the claims below.
* * * * *